THE  LIBRARY 

OF 

THE  UNIVERSITY 

OF  CALIFORNIA 
LOS  ANGELES 


s^^njT^^ 


Skiascopy 


A  Treatise  on  the  Shadow  Test  in  Its  Practical 
Application  to  the  Work  of  Refraction 


EXPLANATION    IN    DETAIL    OF    THE    OPTICAL    PRINCIPLES    ON 
WHICH  THE  SCIENCE   IS   BASED 


WITH  SIXTY-NINE  ILLUSTRATIONS  AND  FOUR  PLATES 


SECOND   EDITION 


PUBLISHED    BY 

THE  KEYSTONE 

THE  ORGAN   OF  THE  JEWEI.RY  AND   OPTICAI^   TRADES 

19TH  &  Brown  Sts.,  Philadelphia,  Pa.,  U.  S.  A. 

1903 

All  Rights  Reserved 


Copyright,  1899,  by  B.  Thorpe 
Publisher  of  The  Keystone 


THIS  TREATISE 


Skiascopy 


GEO.  A.  ROGERS 

Formerly  professor  in  the  Northern  Illinois  College  of  Ophthalmology 

and    Otology,   Chicago  ;      Principal  of   the    Chicago 

Post-graduate  College  of  Optometry,  Lecturer 

and  Specialist  on '  Scientific 

Eye  Refraction, 

is 

recognized  as 

the  clearest  exposition  of  the 

shadow  test  and  most  reliable  guide  on  the 

use  of  the  retinoscope  available  to  the  ophthalmologist. 


Skiascopy 


^  C  O 


PREFACE  TO  SECOND  EDITION 


The  demand  for  a  second  edition  of  this  work  so  soon 
after  the  original  publication  substantiates  every  claim  that 
was  made  for  it  in  the  preface  to  the  first  edition.  Teachers 
and  students  of  optics,  as  well  as  practicing  opticians,  have 
found  it  not  merely  a  guide  and  reference  book,  but  a  thorough 
education  on  the  subject  of  the  shadow  test,  a  complete  mastery 
of  which  is  now  regarded  as  one  of  the  essential  qualifications 
of  every  optician.  In  refraction  work  especially  "a  little 
learning  is  a  dangerous  thing,"  and  the  treatise  which  is  all 
method  and  no  explanation  is  a  good  work  to  avoid.  The 
present  volume  contains  both.  This  second  edition  in  its 
handsome  silk  binding  will  be  a  graceful  as  well  as  a  valuable 
addition  to  the  optician's  library. 


PREFACE  TO  FIRST  EDITION 


The  compilation  of  this  volume  was  undertaken  in  response 
to  a  general  demand  on  the  part  of  oculists  and  opticians  for  a 
work  which  would  cover  the  subject  more  fully  than  any  thus  far 
published.  Any  treatise  on  skiascopy  is  obviously  incomplete 
which  merely  describes  the  method  of  applying  the  shadow  test 
without  satisfactory  explanation  of  the  optical  principles  involved. 

The  works  on  the  subject  thus  far  published  are  open 
to  this  criticism.  The  present  volume  aims  at  supplying  the 
deficiency,  covering,  as  it  does,  not  only  the  method  of  applying 
the  test  and  the  phenomena  revealed  in  its  application,  but  also 
the  why  and  wherefore  of  such  phenomena.  One  can  readily 
understand  that  the  practical  value  to  the  refractionist  of 
skiascopic  manifestations  will  be  greatly  enhanced  by  a  proper 
understanding  of  their  cause  and  the  scientific  principles  con- 
trolling them. 

A  valuable  feature  of  this  work  is  a  description  of  skiascopic 
apparatus,  including  all  the  latest  and  most  improved  instruments 
for  the  use  of  the  refractionist  in  applying  the  test.  Another 
very  serviceable  feature  is  a  copious  index  alphabetically  arranged, 
which  will  greatly  facilitate  reference. 


CONTENTS. 


PAGE. 

Introductory  13 

Popularity  of  Skiascopy.     A  Purely  Optical  Test. 

Chapter  1. 

Subject  Defined  and  Outlined  17 

Elementary  Principles  of  the  Test  and  Their  Application  in 
Skiascopic  Examinations. 

Chapter  2. 

General  Optical  Principles  47 

Notation  of  Light  and  of  Curved  Surfaces.  Dynamic  Prop- 
erties of  a  Wave  of  Light. 

Chapter  3. 

General  Optical  Principles  71 

Refraction  of  the  Eye.  Coef^cient  of  Emmetropia.  The 
Dioptric  Surfaces.    Transition  of  Image  in  Skiascopy. 

Chapter  .}. 

General  Optical  Principles  92 

Focus,  Dififusion,  Aberration,  Inversion  and  Magnification. 

Chapter  5. 

Static  Factors  of  Skiascopy  no 

The  Four  Areas.  The  Three  Intervals.  Subsidiary  Areas 
and  Intervals.    Analysis  of  Static  Factors.     Static  Effects. 

Chapter  6. 

Dynamic  Factors  of  Skiascopy 130 

Tilting  Mirror  and  its  Dynamic  Effects.  Motion  at  Lumin- 
ous Area.  Changing  the  Intervals.  Other  Dynamic 
Principles. 

9 


lO  CONTENTS. 

Chapter  7. 

I'AGE. 

The  Study  of  the  Eye  by  Skiascopy 148 

Emmetropia  and  Symmetrical  Ametropia.  The  Three  Pri- 
mary Cases.     Static  and  Dynamic  Appearances. 

Chapter  8. 

The  Study  of  the  Eye  by  Ski.\scopy 164 

Unsymmetrical  Ametropia.  Regular  Astigmatism.  Irregu- 
lar Astigmatism.  Static  and  Dynamic  Properties.  Patho- 
logical Cases. 

Chapter  9. 

Conditions  Favorable  to  Successful  Work  in  Skiascopy.  ...   1S3 
The    Operating    Room    and    its    Arrangements.       Practical 
Operating  Suggestions  to  Beginners. 

Chapter  10. 

Skiascopic  Devices  and  Inventions  195 

Ingenious  Appliances  Devised  to  Make  the  Method  Mechani- 
cally Perfect  and  Comfortable  for  the  Operator. 

Appendix  211 

Abbreviations,  Symbols  and  Designating  Letters. 

Glossary  of  Optical  Terms  213 

Index    21Q 


INTRODUCTORY. 


A  MONG  all  the  methods  of  practical  optometry  none  has 
-^^^  proved  of  greater  interest  or  incited  closer  study  than 
that  which  is  known  as  skiascopy  or  "the  shadow  test." 
That  this  should  be  the  case  is  not  surprising,  for  by  no  other 
method,  subjective  or  objective,  can  the  full  dioptric  power  of 
an  eye  with  strict  reference  to  the  work  it  is  required,  in  per- 
fect vision,  to  perform  be  so  quickly  and  accurately  measured. 
It  is  safe  to  presume  that  the  method  will  grow  in  favor  from 
year  to  year,  and  that  eventually  no  one  who  cannot  or  will 
not  employ  it  will  attain  the  highest  professional  standing. 

Practically  the  method  is  simple,  but  no  method  goes 
deeper  into  the  fundamental  principles  of  optics  for  its  founda- 
tion. To  learn  to  use  it  practically  is  but  the  work  of  a  few 
days  under  a  competent  instructor,  but  to  understand  the 
varied  and  peculiar  phenomena  made  manifest  in  a  skiascopic 
examination  requires  that  the  optician  or  oculist  be  grounded 
in  the  most  elementary  principles  of  optics,  more  thoroughly 
grounded  than  he  can  be  by  weeks  of  study  of  standard  and 
current  optical  literature.  In  fact,  optical  literature,  as  it  is 
to-day,  does  not  adequately  account  for  some  of  the  appear- 
ances in  skiascopy. 

It  does  not  seem  to  have  been  recognized  that  in  using 
the  method  the  skilled  operator  is  encountering  anything  un- 
usual— anything  that  normal  vision  has  not  encountered  be- 
fore. And  yet  it  is  unquestionably  provable  that  the  ski- 
ascopist  is  looking  really  at  "optical  illusions"  during  the 
critical  period  of  his  examination,  and  that  that  which  he  sees 
has  really  no  objective  existence,  inasmuch  as  it  is  an  effect  at 
his  own  retina — not  at  the  retina  of  the  eye  he  is  examining — 
that  produces  reversal,  and  causes  the  reflex  to  appear  to  move 
in  a  direction  opposite  to  its  actual  motion. 

13 


14  INTRODUCTORY. 

It  is  our  purpose  in  this  work  to  go  more  deeply  into  the 
fundamental  principles  of  optics  upon  which  the  appearances 
in  skiascopy  depend  than  has  heretofore  been  reached;  to 
make  not  only  the  phenomenon  of  reversal,  but  all  the  other 
characteristic  phenomena  of  skiascopy  subservient  to  gen- 
eral optical  laws,  and  to  do  that  the  optical  laws  must  be  am- 
plified somewhat.  This  special  work  we  have  endeavored  to 
bring  into  three  special  optical  chapters  (II.,  III.  and  IV.), 
making  them  the  basis  of  a  closer  study,  in  the  subsequent 
chapters,  of  skiascopic  phenomena. 

The  three  chapters  referred  to  have  no  special  reference 
to  skiascopy,  and  are  equally  applicable  to  all  optical  phe- 
nomena, but  the  student  who  attempts  to  account  for  some  of 
the  most  characteristic  phenomena  of  skiascopy  without  them 
will  be  seriously  handicapped. 

POPULARITY  OF  SKIASCOPY. 

The  popularity  of  skiascopy  as  a  method  of  optometry, 
and  the  enthusiasm  of  those  who  have  taken  the  pains  to  mas- 
ter it  practically,  is  due  to  three  principal  causes — all  of  them 
very  attractive  to  optical  workers.  These  three  chief  at- 
tractions are: 

1.  It  is  an  objective  test. 

2.  It  is  wonderfully  exact. 

3.  It  is  optometrically  complete. 

These  attractions  are  irresistible  to  the  one  who  is  inocu- 
lated with  the  real  professional  zeal. 

To  be  able  to  determine  in  what  direction  an  eye  needs 
lens  help,  and  the  dioptric  power  of  the  lens  required  without 
asking  the  patient  any  questions,  appeals  to  the  sense  of  pro- 
fessional pride.  It  is  prima  facie  evidence  of  more  than  or- 
dinary professional  skill.  It  inspires  confidence,  and  confidence 
creates  a  demand  for  such  services,  and  that  means  increased 
business  and  a  higher  reputation — things  that  no  one  clothed 
in  human  flesh  disdains.  But  there  is  a  satisfaction  in  the  use 
of  the  method  aside  from  its  business-winning  features. 

In  all  subjective  testing  the  oculist  or  optician  depends 
upon  the  testimony  of  one  who,  probably,  has  never  experi- 


INTRODUCTORY.  15 

enced  perfect  vision  for  all  his  guiding  data,  while  by  ob- 
jective methods  the  revelation  of  ametropia  is  to  the  skilled 
observer,  direct.  By  the  former  method  the  patient  in  a  sense 
diagnoses  his  own  case  and  fits  himself.  If  there  is  any  mis- 
take the  patient  is  the  one  to  make  it.  And  how  could  it  be 
otherwise,  since  he  is  called  upon  to  bear  witness  to  something 
that  his  presence  in  the  optical  office  is  a  confession  that  he  is 
incompetent  to  testify  about? 

The  exactness  of  skiascopy  is  due  to  the  fact  that  it  is  a 
dynamic  rather  than  a  static  test.  Motion  or  action,  rather 
than  a  mere  appearance,  is  the  revealing  phenomenon.  We 
may  mistake  appearances,  but  we  are  not  easily  misled  when 
we  judge  a  quantity  or  value  by  motion.  This  is  one  of  the 
most  general  principles  of  guidance  in  the  ordinary  affairs  of 
life.     What  a  thing's  action  is,  that  is  the  thing. 

In  skiascopy  we  judge  the  eye's  condition  by  a  motion 
that  is  developed  apparently  in  the  objective  pupil — the  mo- 
tion of  what  is  termed  the  reflex — the  direction  of  motion 
showing  the  kind,  the  rapidity  of  motion  approximating  the 
amount  of  ametropia.  To  determine  the  exact  amount  it  is 
only  necessary  to  determine  what  lens  power  is  required  to 
cause  motion  to  culminate  and  reverse.  Motion  culminates 
with  the  culmination  of  dif¥usion,  and  the  three  phenomena — • 
culmination  of  motion,  culmination  of  diffusion  and  reversal 
of  motion  are  brought  about  at  one  and  the  same  time. 

It  is  customary  to  speak  of  this  interesting  point  in  a  skia- 
scopic  examination  as  neutralizing  motion,  or  as  reaching  the 
point  of  reversal,  or  as  obtaining  the  maximum  of  dififusion. 
The  one  always  implies  the  others.  The  maximum  of  dif- 
fusion eliminates  the  moving  image  as  such,  leaving  only  an 
illuminated  area  to  move.  Hence,  motion  is  neutralized.  But 
up  to  the  point  of  neutralization  motion  grows  more  and  more 
rapid,  hence  it  is  apparent  that  the  point  of  reversal  is  not 
reached  as  long  as  motion  is  apparent,  and  a  lens  of  higher 
power  is  required  to  neutralize  it. 

But  with  the  culmination  and  elimination  of  motion  dif- 
fusion is  at  its  greatest,  causing  the  reflex  to  appear  as  an  ex- 
tended luminous  area  covering  the  pupil  or  occupying  zones 
of  the  pupil,  and  beyond  this  point  motion  in  the  opposite 


l6  INTRODUCTORY. 

direction  develops,  so  that  there  can  be  no  mistake  about  being 
at  the  point  of  reversal;  or  if  not  at  it  on  which  side  of  it  you 
are.  When  you  reach  such  point  a  simple  calculation  gives 
the  dioptric  assistance  required  by  the  eye  being  examined. 

But  the  method  is  also  dioptrically  complete — that  is,  it 
covers  the  whole  dioptric  ground.  It  is  not  a  partial  measure, 
but  the  measure  of  the  full  dioptric  power  of  the  eye,  includ- 
ing every  dioptric  surface  in  it.  It  is  of  no  importance  in  the 
result  to  know  what  each  surface  does  individually,  but  it  is 
indispensable  to  know  what  all  do  together,  and  this  is  what 
skiascopy  determines. 

A  PURELY  OPTICAL  TEST. 

Skiascopy  is  an  optical  test  in  all  respects.  There  is  no 
question  of  anatomy,  physiology  or  pathology  involved  in  it. 
To  understand  it  thoroughly  requires  a  knowledge  of  the  prin- 
ciples upon  which  the  method  is  based.  It  is  not  enough  sim- 
ply to  know  the  rules.  Rules  are  necessary  for  the  blind,  but 
not  for  those  who  understand  principles.  The  rules  of  skia- 
scopy are  exceedingly  simple,  and  the  general  practical  feat- 
ures of  the  method  may  be  learned  in  one  lesson.  But  skill  in 
the  use  of  the  method  is  obtained  only  by  experience,  and 
knowledge  of  its  fundamental  principles  is  acquired  only  by 
study.  It  is  our  hope  and  expectation  that  the  following  chap- 
ters will  prove  useful  in  extending  knowledge  of  this  exceed- 
ingly interesting  method,  and  lead  to  a  better  understanding 
of  its  fundamental  principles. 


CHAPTER  I. 


SUBJECT  DEFINED  AND  OUTLINED.  ELEMENTARY  PRINCIPLES 
OF  THE  TEST  AND  THEIR  APPLICATION  IN  SKIASCOPIC  EX- 
AMINATIONS. 


OKIASCOPY,  in  its  practical  application,  is  the  art  of  de- 
^^  termining-  the  refractive  condition  of  an  eye  by  the  study 
of  the  reflex  from  the  retina  when  the  image  of  a  luminous 
area  is  cast  upon  it.  In  its  scientific  aspects  it  is  a  branch  of 
the  general  science  of  optics,  being  individual  only  in  its 
method  of  application  of  general  optical  principles.  Simple 
as  the  test  is,  primarily,  there  is  hardly  an  optical  principle, 
or  principle  of  reflection  or  refraction,  that  is  not  made  use  of 
in  it,  for  the  mirror  develops  the  former  while  the  dioptric 
media  of  the  observed  or  observing  eye,  or  both,  develop  the 
latter. 

The  subject  of  skiascopy,  like  all  branches  of  physical 
science,  presents  two  phases  or  aspects  to  the  student.  It  has 
its  static  elements,  features,  limitations  or  qualities,  and  its 
dynamic  properties,  attributes  or  principles.  To  thoroughly 
understand  its  dynamic  elements  the  static  foundation  must 
first  be  thoroughly  understood.  But  before  entering  at  large 
upon  these,  it  will  be  well  to  look  at  the  primary  or  elementary 
practical  features  of  the  test.  We  shall  do  this  entirely  from 
an  opticist's  standpoint,  as  there  is  really  nothing  to  the  test 
that  is  not  wholly  optical,  presuming,  for  the  present,  at  least, 
that  the  reader  is  grounded  in  the  general  optical  principles 
and  nomenclature  which  we  shall  employ. 

observer's   POSITION. 

Skiascopy,  as  defined  above,  implies  an  observer,  one  who 
surveys  from  some  advantageous  position  objective  optical 
phenomena  displayed  upon  the  retina  of  an  observed  eye,  and 

17 


l8  SUBJECT    DEFINED   AND    OUTLINED. 

of  course  through  its  pupil.  It  also  implies  that  such  display 
is  the  image  of  a  luminous  area  of  some  kind.  The  definition 
does  not  state  how  the  observer  is  to  see  such  display,  for  the 
seeing,  rather  than  the  means  employed  to  see,  is  the  essen- 
tial point.  As  a  matter  of  fact  he  does  see  the  display  by  the 
use  of  a  small  circular  mirror  having  a  minute  perforation  in 
its  centre,  called  a  skiascope.  With  this  mirror  he  reflects  pen- 
cils of  light  from  the  luminous  area — back  of  or  at  least  out  of 
the  range  of  vision  of  the  observed  eye — upon  and  around  the 
eve  to  be  examined.  Smaller  pencils  of  these  pencils  are  ad- 
mitted by  the  pupil  of  the  observed  eye,  and  its  dioptric  media 
focus,  as  nearly  as  may  be,  these  pencils  upon  its  retina, 
forming  an  image  of  the  luminous  area  there.  The  skiascop- 
ist  applies  his  eye  to  the  perforation  in  the  mirror,  and  from 
this  point  of  vantage  observes  the  display  upon  the  retina  of 
the  observed  eye  through  its  pupillary  space. 

Why  does  not  the  skiascopist  allow  the  one  under  exam- 
ination to  look  in  a  direction  that  will  give  the  eye  to  be  ex- 
amined pencils  of  light  from  the  luminous  area  direct,  or  with- 
out the  intervention  of  a  mirror;  and  why  does  he  not  observe 
the  pupillary  display  from  an  open  position,  instead  of  handi- 
capping his  observations  with  a  small  peep-hole?  It  is 
because  the  incident  pencils  that  form  the  image  upon  the 
retina  of  the  observed  eye,  and  the  emergent  pencils  by  which 
the  observer  sees  the  pupillary  display,  traverse  the  same 
course  in  opposite  directions.  The  luminous  area,  the  pupil 
of  the  observed  eye  and  the  pupil  of  the  observing  eye  must 
be  in  one  straight  line.  If  the  observing  eye  is  m  front  of  the 
luminous  area  it  and  the  head  obstruct  the  incident  pencils 
by  which  the  image  is  to  be  formed;  if  the  luminous  area  is  in 
front  of  the  observing  eye  it  obstructs  the  emergent  pencils  or 
view  of  the  observing  eye.  The  mirror  may,  however,  be  in 
front  of  the  observing  eye,  and  reflect  pencils  to  the  observed 
eye  as  though  they  came  from  a  point  back  of  the  observer's 
head.  This  answers  the  same  purpose  as  if  they  came  in  fact 
from  that  point.  The  peep-hole  in  the  mirror,  to  which  the 
observer  applies  his  eye,  allows  the  emergent  pencils  to  enter 
the  pupil  of  the  observing  eye  and  thus  obtain  a  view  of  the 
display  at  the  pupil  of  the  observed  eye. 


SUBJECT    DEFINED    AND    OUTLINED.  IQ 

PUPILLARY   DISPLAY. 

The  observed  eye  is  not  directed  to  the  mirror  but  into 
space  at  one  side  of  the  mirror,  since  looking  into  the  mirror 
directly  would  stimulate  the  accommodation  of  the  eye  under 
examination.  But  the  direction  is  near  enough  to  the  mirror 
to  make  its  pupil  accessible  to  the  reflected  pencils  which  fall 
upon  the  eye  and  a  small  area  surrounding  it.  Smaller  pen- 
cils of  these  pencils  enter  the  pupil  and  are  refracted  by  the 
eye's  dioptric  media,  forming  an  image  of  the  luminous  area, 
more  or  less  distinct,  upon  the  retina.  As  the  luminous  area 
is  usually  at  a  finite  distance — i  1-5  to  2  or  3  meters — these 
incident  pencils  would  not  be  exactly  focused  upon  the  retina 
of  an  eye  whose  accommodation  was  passive — that  is,  unless 
it  were  myopic  to  the  exact  degree  required.  An  emmetropic 
eye,  or  a  hyperopic  eye,  or  a  myopic  eye  of  more  or  less  diop- 
tric power  than  would  be  necessary  to  balance  the  incident 
pencils  would  display  an  imperfect  image  upon  the  retina — an 
image  produced  by  diffusion  circles  rather  than  foci.  Such 
an  image  is,  we  may  say,  invariable  under  a  skiascopic  exam.- 
ination.  Even  when  the  eye  is  fully  corrected  by  a  lens,  the 
image  of  the  luminous  area  upon  the  retina,  when  the  accom- 
modation is  passive,  is  imperfect — th&  product  of  diffusion 
circles. 

The  skiascopist  is  not  primarily  concerned  in  the  char- 
acter of  this  image — produced  by  incident  pencils  from  the 
luminous  area — but  in  the  image  at  the  retina  of  his  own  ob- 
serving eye,  produced  by  pencils  emitted  from  or  by  this  im- 
perfect image  through  the  dioptric  media,  the  error  of  which  he 
wishes  to  determine.  These  emitted  or  emergent  pencils  pro- 
duce results  at  his  own  retina,  which  are  projected  into  the 
pupil  of  the  observed  eye,  forming  the  pupillary  display.  The 
two  sets  of  pencils,  incident  and  emergent,  do  not  join  each 
other  point  to  point,  for,  although  there  are  diffusion  circles 
upon  the  retina  of  the  observed  eye,  the  emitted  pencils  start 
from  points,  not  areas,  of  the  retinal  image,  whether  it  be  per- 
fect or  imperfect.  The  potential  foci  of  the  incident  pencils 
may  be  forward  or  back  of  the  retina  of  the  observed  eye,  but 
the  emitted  pencils  start  from  points  upon  the  retina,  whatever 


20  SUBJECT    DEFINED   AND    OUTLINED. 

the  character  of  the  image.  If  the  eye  under  examination  is 
emmetropic,  and  its  accommodation  is  passive,  these  emitted 
pencils  emerge  at  the  cornea  as  neutral  pencils  of  light — that 
is,  they  are  neither  convergent  nor  divergent,  but  consist  of 
plane  waves,  or,  if  you  choose,  of  parallel  rays.  But  if  the  eye 
under  examination  is  hyperopic,  the  pencils  from  the  image 
on  the  retina  are  not  fully  neutralized  by  the  dioptric  media, 
and  emerge  at  the  cornea  as  divergent  pencils — that  is,  they 
consist  of  convex  waves  of  light,  or,  if  you  choose,  of  diverg- 
ent rays.  An  eye  that  is  myopic  emits  pencils,  that,  refracted 
by  its  dioptric  media,  emerge  at  the  cornea  as  convergent 
pencils,  or  pencils  consisting  of  concave  waves,  or,  if  you 
choose,  of  converging  rays.  .  The  pencils  do  not  converge, 
one  to  the  other,  but  since  the  waves  of  which  they  are  com- 
posed are  concave,  their  centers  of  curvature,  or  potential 
foci,  are  somewhere  anterior  to  the  cornea  of  the  observed 
eye.  They  will  form  at  that  point,  or  area,  an  image  of  the 
retinal  image  from  which  they  sprung,  if  allowed  to  reach 
their  foci  without  interruption.  Such  image  may  be  back  of 
the  observing  eye,  at  the  cornea  or  in  front  of  it,  and  between 


Incident  Pencil.— Emmetropia. 


Emergent  Pencil.— Emmetropia. 

the  observed  and  observing  eye.  Upon  its  position  with  refer- 
ence to  the  observing  eye  depends  an  important  primary  skia- 
scopic  manifestation — the  direction  of  motion  of  the  pupillary 
display  when  the  mirror  is  tilted. 

Fig.  I  A  represents  an  incident  pencil  of  light  from  a  finite 


SUBJECT    DEFINED   AND    OUTLINED. 


21 


distance  (one  meter)  being  refracted  by  an  emmetropic  eye 
whose  accommodation  is  passive.  F,  back  of  the  retina,  is  the 
f>otential  focus,  and  a  diffusion  circle  is  upon  the  retina.  Fig. 
I  B  represents  a  pencil  of  light  emerging  from  the  emmetropic 
eye,  or  from  the  image  formed  by  the  diffusion  circles,  when 
the  accommodation  is  passive  The  emergent  pencil  is  neu- 
tralized by  the  eye's  static  retraction,  but  the  incident  pencil 
from  a  finite  distance  is  not  focused  upon  the  retina  by  the 
eye's  static  refraction,  although  a  pencil  from  infinity  would 


Fig.  2. 


M) 


Incident  Pencil.— Hyperopia. 


Emergent  Pencil.— Hyperopia. 


be.  Fig.  2  A  represents  an  incident  pencil  of  light  from  a 
finite  distance  being  refracted  by  a  hyperopic  eye  whose  accom- 
modation is  passive.  The  potential  focus  is  of  course  far  back 
from  the  retina  and  a  larger  diffusion  circle  than  that  formed 
by  the  incident  pencil  in  Fig.  i  A  results.  Fig.  2  B  represents 
a  pencil  of  light  emerging  from  the  hyperopic  eye,  or  from 
the  imperfect  image  produced  by  the  diffusion  circles  of  the 
incident  pencils.  It  starts  at  a  point  in  the  retina,  but  as  the 
eye  is  hyperopic,  or  of  insufficient  static  power,  the  pencil 
emerges  as  a  divergent  pencil,  composed  of  convex  waves  or 
diverging  rays.  In  other  words  the  eye  is  as  defective  in  neu- 
tralizing the  emergent  pencils  as  it  is  in  focusing  incident  pen- 
cils at  F. 


22 


SUBJECT    DEFINED    AXD    OUTLINED. 


Fig.  3  A  represents  an  incident  pencil  of  light  being  re- 
fracted by  a  myopic  eye.  The  myopia  is  slight,  for  the  poten- 
tial focus  is  between  F  (the  focal  point  of  emmetropia)  and 
the  retina,  or  at  F'.  Fig.  3  B  represents  an  emergent  pencil, 
refracted  by  this  myopic  eye.  As  the  pencil  is  a  little  more 
than  neutralized  by  the  refraction  of  the  dioptric  media,  it 
emerges  as  a  slightly  converging  pencil,  composed  of  waves 
the  least  bit  concave,  and  therefore  having  a  potential  real 
focus  anterior  to  the  cornea  of  the  observed  eve.     But  this 


Fig.  3. 


Incident  Pencil.— Slight  Myopia. 


Emergent  Pencil.— Slight  Myopia. 


focus,  if  the  eye  is  less  than  i  D.  myopic — which  it  must  be  in 
the  case  shown  with  the  light  at  one  meter  or  more — is  pos- 
terior to  the  observed  eye  at  one  meter's  distance,  or  to  its 
cornea,  C,  in  the  figure.  In  other  words,  with  both  the  light 
and  the  observing  eye  at  one  meter  its  degree  of  myopia  is  in- 
dicated by  the  position  of  the  potential  focus  of  the  incident 
pencil  forward  of  F,  and  by  the  position  of  the  potential  an- 
terior focus  beyond  one  meter  from  the  cornea  of  the  observed 
eye,  and  therefore  posterior  to  the  cornea  of  the  observing 
eye. 


SUBJECT    DEFINED   AND    OUTLINED. 


23 


Fig.  4  A  represents  a  case  of  myopia  in  which  the  focus 
of  the  incident  pencil  is  at  the  retina,  although  only  the  static 
power  of  the  eye  is  in  use.  A  system  of  pencils  such  as  this 
would  produce  a  perfect  image  of  the  candle  flame  upon  the 
retina,  if  the  candle  flame  were  at  one  meter.  This  eye  would 
show,  by  such  result,  i  D.  of  myopia,  for  with  its  static  power 
it  would  focus  a  pencil  of  light  from  one  meter.  Fig.  4  B  rep- 
resents its  refraction  of  an  emergent  pencil.  The  emergent 
pencil  is  refracted  to  the  same  extent  as  the  incident  pencil,  and 
is  therefore  focused  at  the  same  distance  in  front  of  the  cornea 


Fig.  4. 


rA) 


Incident  Pencil  —Myopia  1  D. 


(  S  ) 


Emergent  Pencil.— Myopia  1  D. 


as  the  light  is,  or  one  meter.  If  the  light  were  a  little  further 
away  the  focus  of  the  incident  pencil  would  be  a  little  forward 
of  the  retina,  but  the  focus  of  the  emergent  pencil  would  be  no 
different— that  is,  for  an  eye  i  D.  myopic.  The  focus  of  the 
emergent  pencil  will  be  at  the  cornea  of  the  observing  eye,  C, 
if  it  is  one  meter  in  front  of  the  observed  eye.  As  all  incident 
pencils  from  the  candle  flame,  and  all  emergent  pencils  from 
the  retinal  image  of  that  flame,  are  refracted  in  that  way,  there 
will  be  in  such  case  a  true  image  of  the  preceding  retinal 


24 


SUBJECT    DEFINED   AND    OUTLINED. 


image  at  the  cornea  of  the  observing-  eye,  or  would  be  if  it  were 
possible  to  have  the  light  and  the  observing  eve  each  at  one 
meter  from  the  observed  eye.  It  is  the  impossibility  of  obtain- 
ing these  conditions  that  classifies  the  pencils  into  incident  and 
emergent  in  skiascopy,  for  they  cannot  coincide  as  in  direct 
vision,  where  the  eye  is  accommodated  for  the  object. 

Fig.  5  A  represents  the  pencil  of  light  as  being  focused 
forward  of  the  retina,  at  F'.  This  eye  is  more  than  i  D.  my- 
opic. The  image  at  the  retina  will  not  be  perfect,  for  it  will 
be  formed  of  diffusion  circles,  the  same  as  the  image  in  Fig. 


Incident  Pencil.— Myopia,  above  1  D. 


Emergent  Pencil— Myopia,  above  1  D. 


3  A,  only,  in  this  case,  the  foci  of  the  pencils  are  forward  of  the 
retina  instead  of  back  of  it.  To  place  the  foci  of  the  incident 
pencils  upon  the  retina,  the  eye  must  be  myopic  to  that  pre- 
cise degree  represented  by  the  distance  of  light.  If  the  light 
is  2  meters  distant  and  the  eye  is  ^  D.  myopic,  the  image  on 
the  retina  will  be  perfect.  If  the  light  is  ^  meter  distant 
;and  the  eye  is  2  D.  myopic,  the  same  result  will  be  obtained. 
But  in  either  of  these  cases,  or  in  any  case  of  myopia,  the 
emergent  pencils  will  be  convergent.  Fig.  5  B  represents  the 
refraction   of  a  pencil   of   light   emerging  from   the   eye   in 


SUBJECT    DEFINED    AND    OUTLINED.  25 

Fig.  5  A.  As  the  eye  is  more  than  i  D.  myopic  the  anterior 
focus  of  this  pencil  is  nearer  than  one  meter,  or  forward  of  the 
observing  eye  if  at  one  meter,  or  between  the  observed  and 
observing  eye.  As  all  pencils  of  light  whether  incident  or 
emergent,  will  follow  the  same  rule  as  these  pencils,  there  will 
be,  between  the  observed  and  observing  eye,  all  the  conditions 
essential  for  the  formation  of  a  true  image  there.  A  true 
image  v^ll  be  there  in  fact,  a  real  and  physical  image,  although 
no  screen  or  reacting  surface  displays  it.  It  is  an  image  of  the 
image  upon  the  retina  of  the  observed  eye.  As  the  image 
upon  the  retina  of  the  observed  eye  is  inverted  this  "aerial" 
image  will  be  erect.  As  the  aerial  image  is  erect,  and  it  is 
from  it  that  the  observing  eye  receives  its  pencils,  the  image 
upon  the  retina  of  the  observing  eye  will  be  inverted — an  in- 
verted image  of  the  candle  flame.  And  thus  you  have  the  re- 
fractive effects  of  all  classes  of  eyes  whose  ametropia  is 
symmetrical  or  equal  in  all  meridians.  The  case  represented 
in  Fig.  4  B  is  of  special  skiascopic  interest,  as  it  shows  the 
position  at  which  reversal  of  motion  takes  place  with  the 
observing  eye  at  one  meter. 

STATIC  ELEMENTS. 

It  is  seen  that  skiascopy  presents  seven  static  factors  or 
elements  for  study.  These  factors  consist  of  four  areas  and 
three  intervals.     The  four  areas  are  as  follows: 

1.  The  luminous  area. 

2.  The  mirror. 

3.  The  retina  of  the  observed  eye. 

4.  The  retina  of  the  observing  eye. 

And  the  intervals  consist  of  spaces  as  follows: 

1.  The  space  from  area  i  to  area  2. 

2.  The  space  from  area  2  to  area  3. 

3.  The  space  from  area  3  to  area  4. 

As  area  i,  though  in  front  of  the  mirror,  has  the  effect, 
by  the  reflection,  of  being  behind  it,  intervals  i  and  2  together 
form  the  space  in  which  the  incident  pencils  are  developed  be- 
fore reaching  the  cornea  of  the  observed  eye,  and  area  i  is 
eliminated.     But  as  area  2  and  area  4  are  practically  coinci- 


26  SUBJECT    DEFINED   AND    OUTLINED. 

dent  in  position,  intervals  2  and  3  are  practically  equal  in  ex- 
tent. As  pencils  of  light,  in  passing  across  these  spaces,  are 
in  homogeneous  air  only  prior  to  entering  or  subsequent  to 
emerging  from  a  cornea,  the  corneas  of  the  observed  and  ob- 
serving eye  are  the  real  limits  in  which  the  pencils  may  be 
developed  naturally,  and  intervals  2  and  3  are  shortened  by  .1 
space  equal,  in  the  former  case,  to  the  diameter  of  the  observed 
eye,  and  in  the  latter  by  the  diameters  of  both  the  observed  and 
the  observing  eye.  These  spaces  are  trifling  in  themselves: 
but  are  noted  that  accurate  conclusions  may  be  drawn.  We 
shall  have  occasion  to  deal  with    these    static    factors    more 


Fig.  6. 


-  -  ^-^''  ' 


static  Factors.— Skiascopy.  4  Areas  and  3  Intervals. 

completely  in  a  subsequent  chapter.       Fig.  6  illustrates  the 
four  areas  and  three  intervals. 

DYNAMIC  FACTORS. 

By  a  dynamic  principle  in  optics  those  phenomena  that 
result  from  and  during  the  change  of  a  static  factor  are  meant. 
Dynamic  factors  result  from  motion  of  static  factors.  The 
mere  shift  from  one  static  foundation  to  another,  as  the  short- 
ening or  lengthening  of  an  interval,  is  not  dynamic  except  in 
the  phenomena  that  result  from  and  during  the  change  of  posi- 
tion. If  any  of  the  areas  above  is  given  motion  and  the  ob- 
serving eye  studies  the  effects  or  optical  phenomena  resulting 
from  such  motion  during  the  motion,  dynamic  phenomena 
appear.  This  may  be  accomplished  by  motion  of  the  lumin- 
ous area,  by  lateral  motion  of  the  observed  eye,  by  lateral  mo- 
tion of  the  observing  eye,  by  shortening  or  lengthening  inter- 
vals, or   by   motion   of   the   mirror.      The  latter  is  the  mode 


SUBJECT    DEFINED   AND    OUTLINED. 


27 


ordinarily   employed    in    skiascopy   to    evolve   dynamic   phe- 
nomena. 

TILTING  THE   MIRROR. 

The  mirror  receives  only  a  small  part  or  portion  of  each 
pencil  emitted  by  the  luminous  area.  The  rest  of  each  of 
these  pencils  is  dissipated  in  the  darkened  room.  The  mirror 
is  so  held  as  to  reflect  the  pencils  it  receives  upon  the  eye  and 
the  face  of  the  one  whose  eye  is  being  examined.  But  only  a 
small  portion  of  each  reflected  pencil  is  admitted  into  the  eye 
under  observation.  We  may  call  the  pencils  reflected  by  the 
mirror  the  major  pencils  and  those  admitted  into  the  eye  the 
minor  pencils.     If  the  mirror  is  tilted  the  major  pencils  are 


Fig.  7. 


reflected  in  a  different  direction,  and  the  "light  on  the  face" 
moves  about.  Its  motion  is  actual  and  due  to  a  change  in  the 
angle  of  incidence  which  causes  a  change  in  the  direction  of 
the  reflected  major  pencils.  But  as  a  result  of  their  motion 
and  change  of  direction,  the  observed  eye,  if  still  within  range 
of  these  pencils,  will  receive  an  entirely  new  set  of  minor  pen- 
cils, also  pursuing  a  slightly  different  direction  than  these  that 
have  passed  ofif.  This  causes  the  image  upon  the  retina  of  the 
observed  eye,  which  is  fixed  in  its  direction,  to  move  when  the 
mirror  moves.     To  the  observed  eye,  the  virtual  image  in  the 


28  SUBJECT    DEFINED   AND    OUTLINED. 

mirror,  which  is  nothing  more  than  a  projection  of  its  retinal 
image,  appears  to  move,  when  the  mirror  is  moved,  in  a  direc- 
tion contrary  to  the  actual  motion  of  the  major  pencils  and 
the  image  upon  its  own  retina.  This  is  due  to  the  principle 
of  inversion  in  projection,  the  principle  that  causes  an  image 
on  the  right  area  of  a  retina  to  be  projected  to  a  left  position 
in  the  world,  and  vice  versa. 

If  the  plane  mirror  is  so  tilted  as  to  cause  the  reflected 
major  pencils  and  "light  on  the  face"  to  move  to  the  right  (the 
observer's  not  the  observed's  right)  the  image  on  the  retina 
of  the  observed  eye,  no  matter  whether  it  be  myopic,  hyper- 
opic  or  emmetropic,  will  move  to  the  right  also.  The  image 
moves  with  the  mirror — that  is,  it  moves  with  the  "light  on  the 
face,"  or  in  the  same  direction.  (See  Fig.  8.)  By  the  "same' 
direction,  that  direction  which  is  in  harmony  with  the  motion 
of  the  mirror  is  meant.  Two  opposite  felloes  on  the  same 
wheel  move  in  the  same  direction,  although  in  a  sense  their 
motion  is  contrary  to  each  other.  That  is  because  of  their 
opposite  positions,  not  because  of  their  opposite  motions.  Tf 
the  light  on  the  face  moves  upward  or  downward  or  to  the  left, 
the  image  upon  the  retina  of  the  observed  eye  goes  in  the  same 
direction.  From  the  standpoint  of  the  one  under  examination 
the  virtual  image  appears  to  move  contrary  to  the  tilting  of  the 
mirror,  but  we  are  not  writing  for  the  benefit  of  any  one  but 
the  observer,  and  the  appearances  and  motions  from  his 
standpoint  are  the  essential  phenomena. 

VIEW   OF   OBSERVER. 

But,  nowithstanding  the  harmony  of  motion  explained 
above,  to  the  observer  the  motion  of  the  image  and  of  the  dark 
areas  that  surround  it  will  appear  to  be — under  certain  condi- 
tions— directly  contrary  to  this  rule.  When  the  "light  on  the 
face"  moves  to  the  right,  the  pupillary  display  in  the  observed 
eye  moves,  or  appears  to  move,  to  the  left.  (See  Fig.  9.)  This 
phenomenon  (with  a  plane  mirror)  only  occurs  when  the  ob- 
served eye  is  myopic,  and  its  emergent  pencils  focus,  as  shown 
in  Fig.  5  B,  in  front  of  the  observing  eye.  The  motion  of  the 
retinal  image  is  all  right,  but  the  observer  views  this  image 


SUBJECT    DEFINED   AND    OUTLINED. 


29 


and  its  motion  throug-h  an  imperfectly  focused  lens  or  micro- 
scope— the  dioptric  media  of  the  observed  eye.  If  the  eye  is 
myopic  the  lens  is  more  powerful  than  the  work  it  has  to  do. 
We  may  consider  that  it  is  too  far  away  from  die  object,  and 
the  pencils  it  emits  from  that  object — the  imperfect  retinal 
image — emerge  from  the  cornea  as  convergent  pencils.  They 
focus  and  form  a  true  image  anterior  to  both  the  observed 
and  observing  eye — that  is,  between  them. 

The  true  image  thus  formed  in  front  of  the  observing  eye 
is  an  inversion  of  the  preceding  retinal  image.  All  the  pencils 
of  light  emitted  by  the  observed  eye  are  transposed  at  this 
true  image,  and  "forwarded"  in  this  form  to  the  observing  eye. 
The  image  directly  in  front  of  the  observing  eye  is  the  im- 
mediate source  of  the  pencils  that  reach  the  observing  eye,  the 
same  as  the  retinal  image  is  the  immediate  source  of  the  pen- 


FiG.  8. 


Fig.  9. 


cils  emitted  from  the  observed  eye.  The  observing  eye,  if  not 
too  near  this  aerial  image,  focuses  these  transposed  pencils  and 
a  re-inverted  image  appears  upon  the  retina  of  the  observing 
eye.  As  a  result  we  trace  the  inversions  as  follows :  The  lum- 
inous area  is   erect,   but  the  image   upon  the  retina  of  the 


30  SUBJECT    DEFINED    AND    OUTLINED. 

observed  eye  is  inverted;  the  first  retinal  image  is  inverted  but 
the  aerial  image  is  therefore  erect;  since  the  aerial  image  i? 
erect  the  image  at  the  retina  of  the  observing  eye  is  inverted. 
The  two  retinal  images  are  therefore  the  same  in  position. 
Now,  when  the  image  upon  area  3  moves  to  the  right  (the  ob- 
server's right)  the  image  upon  area  4  (the  observer's  own 
retina)  moves  to  the  right  also.  The  observer  projects  this 
motion  upon  his  retina  as  motion  to  the  left,  for  the  same  rea- 
son and  under  the  same  principle  that  the  person  under  exam- 
ination projects  motion  of  the  image  upon  his  retina,  the  vir- 
tual image,  as  motion  in  the  opposite  direction. 

This  reverse  direction  of  motion  may  appear  clearer  with- 
out tracing  the  effect  at  area  4,  thus :  When  the  image  on  area 
3  moves  to  the  right  the  true  image  in  front  of  the  observing 
eye  moves  to  the  left,  because  it  is  an  inverse  image  of  the 
retinal  image  at  area  3.  As  the  newly  transposed  pencils  come 
to  the  observing  eye  from  a  position  further  to  the  left,  the 
image  or  display  appears  to  move  in  that  direction.  It  is  as 
though  an  object  in  front  of  the  observer's  eye  actually  moved 
to  the  left.  It  would  of  course  appear  then  to  move  to  the  left, 
although  the  image  upon  his  retina  would  move  to  the  right 
as  heretofore  noted.  But  if  the  pencils  are  not  focused  in 
front  of  his  eye  they  are  focused  more  or  less  accurately  upon 
his  retina,  and  his  retina  receives  the  first  inverted  image  pro- 
duced by  the  pencils  from  area  3.  Motion  on  his  retina  is  then 
opposite  to  that  at  area  3. 

AREA   OF   REVERSAL. 

The  area  of  reversal  is  the  position  of  the  aerial  image, 
wherever  it  may  be.  Real  reversal  of  motion  appears  only  when 
the  observing  eye  is  far  enough  back  of  the  area  of  reversal  to 
obtain  something  like  an  image  upon  its  retina.  If  the  ob- 
serving eye  is  at  or  very  near  the  area  of  reversal,  the  image 
upon  its  retina  is  so  diffuse  in  character — composed  as  it  is 
of  large  diffusion  circles — that  nothing  but  a  radiance  or  glow 
appears  in  the  pupillary  space.  But  at  a  point  a  little  forward 
or  back  of  the  area  of  reversal,  the  observing  eye  may  get  a 
sufficiently  good  image  of  the  light  within  the  observed  eye 


SUBJECT    DEFINED    AND    OUTLINED.  3I 

to  discover  the  direction  of  motion  at  the  pupil,  and  if  forward 
of  it  get  corresponding  motion;  but  at  a  point  a  little  back  oi 
the  area  of  reversal  it  will  be  able  to  get  reverse  motion  only. 
The  first  and  primary  work  of  the  skiascopist  is  to  find  the 
area  of  reversal.  If  the  eye  under  observation  is  emmetropic 
or  hyperopic  there  will  be  no  anterior  image,  and  if  it  is  but 
slightly  myopic  the  potential  anterior  image  will  be  back  of 
the  observing  eye.  But  by  placing  a  plus  lens  in  front  of  the 
eye  under  observation,  and  increasing  the  power  of  the  lens, 
the  observed  eye  may  be  made  artificially  myopic — suffi- 
ciently myopic  to  bring  the  area  of  reversal  to  a  position  in 
front  of  the  observing  eye. 

This  is  the  plan  of  procedure  in  skiascopy.  The  first 
and  primary  purpose  is,  with  or  without  a  lens  as  the  case 
may  require,  to  get  the  area  of  reversal  at  the  cornea  of  the 
observer.  If  he  is  one  meter  from  the  observed  eye  and  the 
area  of  reversal  is  at  his  cornea,  the  observed  eye,  with  or 
without  a  lens,  as  the  case  may  be,  is  one  diopter  myopic.  If 
it  takes  a  +  3  D.  lens  to  locate  the  area  of  reversal  at  this 
point,  the  eye  under  examination  is 

-3  D. 
+  I  D.   . 


-2D. 


two  diopters  hyperopic.  The  —  3D.  used  above  expresses 
the  eye's  deficiency  (skiascopically)  in  giving  the  skiascopist 
what  he  wants — the  area  of  reversal  at  one  meter.  The  +  i  D. 
expresses  the  over  dioptric  power  of  an  eye  that  would  give 
him  w^hat  he  requires.  The  sum  of  these  two,  —  2D.  ex- 
presses the  eye's  dioptric  deficiency.  It  would  take,  of  course, 
a  +  2  D.  lens  to  overcome  a  —  2D.  deficiency,  and  +  2  D. 
would  be  the  lens  required. 

GETTING  REVERSAL. 

In  working  out  a  case,  then,  the  skiascopist's  first  or 
primary  purpose  is  to  bring  the  area  of  reversal  to  his  cornea, 
or  to  determine  what  lens  would  be  or  is  necessary  to  produce 
that  result.     But  when  the  area  of  reversal  is  at  his  cornea 


32  SUBJECT    DEFINED    AND    OUTLINED. 

he  sees  no  image  at  all  in  the  pupillary  space,  but  only  a  glow, 
nor  can  he  tell  whether  motion  is  one  way  or  the  other,  for 
there  is  no  motion  if  there  is  no  image,  of  course.  He  getj> 
the  primary  result  by  gauging  the  two  opposite  positions.  If, 
with  a  +  2.75  D.  lens  there  is  very  rapid  corresponding  mo- 
tion, a  +  3  D.  lens  will  probably  eliminate  both  the  image  or 
pupillary  display,  and  motion  also.  A  +  3.25  D,  may  then 
give  very  rapid  reverse  motion.  The  area  of  reversal,  with  a 
+  2.75  D.,  is  then  back  of  the  cornea,  but  with  a  +  3.25  D.  it  is 
in  front  of  the  cornea.  With  a  +  3  D.  and  the  total  disappear- 
ance, as  it  were,  of  pupillary  display,  there  is  no  doubt  but  that 
the  area  of  reversal  is  at  the  cornea.  Perhaps  .12^  D.  may 
bring  the  results  nearer — that  is,  a  +  2.87^  D.  lens  may  still 
give  motion  with  the  mirror  and  a  +  3.12^  D.  may  reverse  the 
motion.  In  that  case  +  3  D.  is  undoubtedly  the  lens  required 
to  bring  the  area  of  reversal  to  the  cornea. 

The  above  is  but  an  example.  It  may  take  minus  lenses 
to  bring  the  area  of  reversal  to  the  cornea,  as  a  —  2D.  lens, 
or  it  may  take  a  stronger  plus  lens,  as  a  +  5  D.  or  +  8  D.  But 
in  any  of  these  cases  the  procedure  is  the  same.  If  the  eye 
under  observation  shows  the  opposite  motion — or  motion 
against  the  mirror — to  start  with,  it  is  certainly  myopic,  and 
sufficiently  myopic  to  place  the  image,  or  area  of  reversal,  be- 
tween the  observed  and  the  observing  eyes.  In  this  case  the 
skiascopist  places  minus  lenses  before  it  to  bring  the  area 
of  reversal  back  to  his  cornea.  If  a  —  1.75  D.  lens  still  gives 
opposite  motion,  a  —  2D.  lens  will  possibly  stop  it.  It  may 
even  reverse  the  motion,  or  make  it  with  the  mirror.  If  —  2 
D.  lens  gives  motion  with  the  mirror  and  —  1.75  D.  gives 
motion  against  it,  a  —  1-87^  D.  would  undoubtedly  neutralize 
all  motion  and  cause  the  pupillary  display  of  motion  to  dis- 
appear. The  area  of  reversal  would  be  at  the  cornea  of  the 
observing  eye,  or  so  near  it  that  a  more  exact  location  could 
not  be  found. 

RAPIDITY   OF  MOTION. 

The  apparent  motion  as  seen  at  the  pupil  of  the  observed 
eye  is  slowest  when  the  area  of  reversal  is  farthest  from  the 
cornea  of  the  observing  eye.     As  lenses  are  added  bringing 


SUBJECT    DEFINED   AND    OUTLINED.  33 

the  area  of  reversal  nearer  to  the  observing  eye,  motion  at  the 
pupil  of  the  observed  eye  grows  more  rapid.  It  is  most  rapid 
just  before  the  pupillary  display  or  motion  at  the  pupil  dis- 
appears altogether.  The  nearer  the  skiascopist  gets  to  his 
primary  result  the  more  distinctly  marked  is  the  motion.  This 
is  a  great  point  in  the  test,  especially  for  fine  degrees  of  error. 
He  knows  when  the  case  gets  "hot"  or  "cold"  by  the  rapidity 
of  motion.  If  the  motion  is  very  sluggish  he  wastes  no  time 
on  weak  lenses,  but  takes  a  5  D.  or  even  an  8  or  10  D.  lens  to 
start  with.  If  it  is  too  strong  it  is  as  easy  to  weaken  it  by  less 
powerful  lenses  as  to  strengthen  a  too  weak  lens.  In  a  little 
while  he  gets  so  well  acquainted  with  the  degree  of  motion  for 
different  degrees  of  error,  that  he  will  be  able  to  take  a  lens 
within  .50  D.  of  what  he  wants  to  start  with.  It  then  takes  but 
one  change  usually  to  get  exactly  what  he  is  in  search  of. 

The  difficulties  that  will  beset  beginners  in  the  practice  of 
this  test  will  be  chiefly  in  obtaining  this  primary  result — ^bring- 
ing the  area  of  reversal  to  the  cornea.  The  pupillary  space 
which  they  see  will  seem  "dreadfully"  small  in  which  to  ob- 
serve motion.  And  when  they  get  near  to  the  primary  result, 
if  they  ever  do,  the  motion  will  be  so  "lightning"  like  that 
"where  it  comes  from  and  whither  it  goetli"  will  be  like  ask- 
ing the  source  and  destination  of  sheet  lightning,  as  seen 
in  the  horizon  on  a  summer's  evening.  But  practice  will 
sharpen  the  perceptive  faculties — practice  with  the  schematic 
e)'e  to  begin  with  and  later  with  human  eyes.  The  confusing 
reflections  at  first  noticed  will  soon  be  eliminated  and  close 
work  begin  to  be  done. 

CAUSE  OF  RAPID  MOTION. 

The  cause  of  rapidity  of  motion,  as  the  area  of  reversal  is 
brought  near  to  the  cornea  of  the  observing  eye,  is  not,  as  a 
well-known  writer  on  the  subject  asserts,  due  to  magnifica- 
tion, but  simply  to  the  nearness  of  the  immediate  source  of 
light  to  the  observing  eye — the  image  which  constitutes  the 
area  of  reversal.  It  is  precisely  upon  the  same  principles  that 
a  near  object,  moving  with  the  same  speed  as  a  distant  object, 
passes  across  the  field  of  vision  more  rapidly.     We  know  the 


j4  SUBJECT    DEFINED   AND    OUTLINED. 

object  is  near  us,  and  so  do  not  consider  its  motion  rapid  be- 
cause its  image  passes  across  the  retina  rapidly.  But  this 
aerial  image,  slight  though  its  actual  motion  may  be,  is  pro- 
jected into  the  pupil  of  the  observed  eye.  It  may  be  an  inch 
from  the  cornea,  but  a  very  slight  motion  on  its  part,  projected 
to  a  point  a  meter  or  so  away,  seems  very  rapid.  It  is  rapid 
in  crossing  the  field  of  vision.  If  we  could  know  it  was  so 
near,  however,  it  might  be  just  as  hard  to  see  it,  but  we  would 
not  refer  it  to  a  point  so  far  away  and  would  therefore  judge 
its  real  motion  more  accurately.  One  may  pass  his  hand  be- 
fore the  eye  at  a  point  so  near  that  it  flashes  across  the  field 
of  vision  quite  as  quickly  as  this  image  when  the  area  of  re- 
versal is  near.     There  is  no  difference  in  the  two  cases. 

THE  FINAL  CORRECTION. 

But  bringing  the  area  of  reversal  to  the  cornea  does  not 
dispose  of  the  case.  The  final  correction  must  be  added  to 
complete  the  whole.  If  an  eye  with  a  plus  lens  before  it  has 
an  anterior  image  it  is  artificially  myopic — how  myopic  de- 
pends upon  the  distance  of  the  anterior  image.  If  it  is  one 
meter  from  the  observed  eye,  that  eye  is  artificially  myopic 
I  D.  It  is  necessary  then  to  add  —  i  D.  to  the  lens  which 
brings  the  area  of  reversal  to  that  point.  If  such  lens  is  a  -r 
4  D.  the  addition  is  simple,  for 

+  4D. 
-  I  D. 


+  3D- 
is  the  complete  correction.     If  the  primary  lens  is  a  —  5  D., 
for  instance,  the  correction  is 

-5D. 

—  I  D. 


—  6  D. 


all  told.  But  the  observer  may  choose  a  greater  or  less  dis- 
tance than  one  meter.  If  the  distance  is  two  meters,  then  the 
observed  eye  has  been  made  by  the  lens  in  front  of  it  ^  or  .5 
D.  artificially  myopic.     In  that  case  —  .5  D.  should  be  added 


SUBJECT    DEFINED    AND    OUTLINED.  35 

to  the  primary  lens.  If  ^  meter  is  the  distance  of  observation 
—  2D.  should  be  added  to  the  primary  lens.  Whatever  the 
distance  of  the  observers,  the  final  correction  should  be  for  as 
many  diopters  as  the  reciprocal  of  the  distance  in  meters. 

When  the  final  correction  has  been  added  the  eye  will  be 
the  same  in  refractive  power  as  an  emmetropic  eye.  It  will  be 
artificially  emmetropic,  which  is  the  precise  result  wanted. 
W'ith  its  correction  all  on,  viewed  skiascopically  the  pupillary 
display  will  be  the  same  as  that  of  an  emmetrope.  The  image 
or  pupillary  figure  will  move  with  the  mirror.  An  expe- 
rienced skiascopist  can  tell  very  closely  what  this  motion 
should  be,  without  going-  to  the  trouble  of  making  the  primary 
results  appear.  It  is  safer,  however,  to  follow  the  routine  de- 
scribed, for  no  two  emmetropic  eyes,  or  hardly  a  pair  of  emme- 
tropic eyes,  are  alike,  except  in  being  emmetropic.  Their 
dioptric  power  differs  because  their  anterio-posterior  diam- 
eters differ.  But  getting  the  primary  lens  with  great  accu- 
racy is  the  special  fine  point  in  skiascopy.  It  is  there  that  the 
error  is  really  measured.  Adding  the  secondary  result  to  that, 
for  the  purpose  of  completing  the  correction,  is  perfunctory — 
according  to  set  rule.  Unless  the  primary  modification  is 
made  with  delicacy  and  exactness,  the  secondary  or  final  mod- 
ification will  not  make  the  whole  result  exact. 

THE   INCIDENT   PENCILS. 

In  neither  of  the  corrections  above,  primary  or  second- 
ary, is  any  attention  paid  to  the  incident  pencils.  They  are 
of  course  modified  at  the  same  time  and  to  the  same  degree 
as  the  emergent  pencils  when  lenses  are  placed  before  the  ob- 
served eye,  but  the  purpose  of  the  skiascopist  is  not  to  produce 
a  perfect  image  on  area  3  by  the  lens,  but  to  secure  correct 
emergent  pencils.  When  the  accommodation  is  passive  and 
the  luminous  area  is  nearer  the  observed  eye  than  infinity,  a 
lens  in  front  of  the  eye  will  not  focus  the  incident  pencils  and 
neutralize  the  emergent  pencils  at  the  same  time.  The  lens 
that  neutralizes  the  emergent  pencils  causes  the  incident  pen- 
cils to  focus  posterior  to  the  retina,  and  therefore  gives  rise  to 
circles  of  diffusion  and  an  imperfect  image  at  area  3.  The 
primary  lens,  which  brings  the  area  of  reversal  to  the  cornea. 


36  SUBJECT    DEFINED   AND    OUTLINED. 

more  nearly  focuses  the  incident  pencils  upon  the  retina.  But 
it  doesn't  exactly  focus  them,  because  the  sum  of  intervals  i 
and  2  are  always  a  little  more  than  interval  3,  since  interval  2 
equals  interval  3.  The  nearer  the  luminous  area  is  to  the 
mirror  the  more  nearly  are  the  foci  of  the  incident  pencils 
placed  upon  the  retina  with  the  primary  lens.  The  more  dis- 
tant the  luminous  area  is  from  the  mirror  the  more  nearly  the 
incident  pencils  focus  upon  the  retina  with  complete  correc- 
tion. 

It  is  seen,  then,  that  in  skiascopy,  the  two  sets  of  pen- 
cils, incident  and  emergent,  are  never  quite  together,  point  to 
point,  upon  the  retina,  except  in  myopia  of  the  exact  degree 
required  to  focus  the  incident  pencils.  But  when  the  cor- 
rected eye  views  ordinary  objects,  whether  luminous  or  non- 
luminous,  and  whether  w^th  or  without  the  use  of  the  accom- 
modation, the  two  sets  of  pencils  are  together,  point  to  point, 
for,  whatever  engages  the  vision,  the  eye  is  accommodated  to 
that  distance  and  focuses  the  incident  pencils  upon  the  retina. 
The  emergent  pencils  are  in  like  manner  focused  at  the  object. 
These  pencils  are  disjoined  in  skiascopy  by  giving  the  eye 
divergent  pencils  while  the  accommodation  is  passive.  The 
direction  of  the  visual  axis  does  not  allow  these  pencils  to 
center  at  the  macula,  although  diffusion  circles  may  spread 
over  the  macula.  It  is  essential  in  making  the  test  without  a 
mydriatic  that  the  accommodation  be  not  stimulated  into 
action.  Hence,  the  necessity  that  the  eye  be  directed  to  one 
side  of  the  mirror  that  the  incident  pencils  may  not  fall  where 
they  would  (unless  the  person  under  examination  knows  how 
to  avoid  it)  stimulate  the  accommodation.  Such  stimulus  may 
be  neutralized  by  will  power,  but  it  is  hardly  to  be  expected 
that  a  person  being  examined  would  know  how,  or  attempt  if 
he  did  know,  to  neutralize  the  stimulus.  A  means  may  be 
found  of  removing  any  danger  of  such  action  being  excited. 
Of  such  means  we  shall  speak  in  the  future. 

REGULAR  ASTIGMATISM. 

Astigmatism  is  want  of  symmetry  in  the  refracting  power 
of  the  eye  for  dififerent  meridians.  Either  or  both  principal 
meridians  may  be  hyperopic,  either  or  both  myopic,  or  one 


SUBJECT    DEFINED    AND    OUTLINED.  37 

meridian  may  be  hyperopia  while  the  other  is  myopic.  As  the 
refraction  of  the  eye  is  positive  in  all  meridians,  astigmatism 
merely  shows  that  positive  refraction  is  greater  in  one  meridian 
than  the  other.  If  the  meridian  of  greatest  power  is  emme- 
tropic, the  meridian  of  least  power  is  hyperopia,  and  all  the  me- 
ridians between  shade  down  from  the  most  hyperopia  meridian 
to  the  emmetropic  meridian.  But  if  the  meridian  of  least  power 
is  emmetropic,  the  meridian  of  greatest  power  is  myopic,  and 
the  other  meridians  shade  down  from  the  most  myopic  merid- 
ian to  the  emmetropic  meridian.  If  the  astigmatism  is  com- 
pound there  is  simply  over-  or  under-power  in  both  meridians, 
but  a  greater  over-  or  under-power  in  one  than  in  the  other. 
The  astigmatic  element  of  the  refractive  error  is  really  not  com- 
pound but  simple,  for  it  is  the  difference  of  the  two  meridians, 
and  that  difiference  is  no  greater  and  no  less  nor  more  com- 
plicated because  both  are  wrong.  A  correction  of  one  me- 
ridian by  a  spherical  lens  may  bring  the  other  meridian  nearer 
to  correct  refraction,  but  if  the  astigmatism  is  mixed,  the  cor- 
rection of  one  meridian  by  a  spherical  lens  augments  the  error 
of  the  other. 

Primarily  the  correction  of  astigmatism  by  skiascopy 
follows  the  same  order  as  the  correction  of  symmetrical  ame- 
tropia, but  the  primary  correction  is  first  of  one  meridian — 
either  the  meridian  of  greatest  or  least  power,  or  the  meridian 
of  greatest  or  least  error.  A  spherical  lens  is  sought  which 
will  bring  one  of  the  principal  areas  of  reversal — for  there  ii 
an  area  of  reversal  for  each  meridian,  both  principal  and  sec- 
ondary— to  the  cornea  of  the  observing  eye.  The  remaining 
primary  correction  must  be  made  with  a  cylinder,  a  cylinder 
that  will  bring  the  other  areas  of  reversal — both  that  of  the 
other  principal  meridian  at  right  angles  to  the  first,  and  those 
of  all  intermediate  meridians — to  a  position  of  coincidence 
with  the  area  of  reversal  of  the  primarily  corrected  meridian. 
This  eliminates  the  astigmatism  and  leaves  only  the  secondary 
or  final  correction  to  make  the  correction  complete.  This 
final  correction  will  be  spherical,  or  symmetrical  for  all  merid- 
ians. There  are  in  all  cases  of  regular  astigmatism  two  prin- 
cipal meridians  at  right  angles  to  each  other,  but  each  inter- 
mediate meridian  has  power    in    proportion    to    its    position 


38  SUBJECT    DEFINED   AND    OUTLINED. 

between  the  two  principal  meridians.  If  an  eye  is  3  D.  hyper- 
opic  in  the  vertical  meridian  and  2  D.  hyperopia  in  the  hori- 
zontal, the  astigmatic  element  is  i  D.  But  meridian  45°,  mid- 
way between  90°  and  o,  is  2^  D.  hyperopia  and  meridian  60°, 
75°,  etc.,  are  less  than  3  D.  but  more  than  2^  D.  hyperopia, 
shading  gradually  from  2  D.  at  o  or  180°  to  90°.  A  +  2  D.  sph. 
corrects  hyperopia  in  the  horizontal  but  leaves  i  D.  in  the 
vertical.  In  that  case  the  intermediate  meridians  have  a  dif- 
ferent dioptric  power,  but  shade  from  o  D.  in  0°  to  i  D.  in 
90°.  The  rule  for  the  intermediate  meridians  will  be  given  in 
Chapter  VIII.,  as  it  is  only  desired  here  to  show  that  sphericals 
change  the  dioptric  power  of  all  meridians,  but  do  not  affect 
the  astigmatic  element.  A  +  3  D.  sph.  would  neutralize  90° 
but  produce  —  i  D.  in  meridian  180°. 

Corresponding  to  the  two  principal  meridians  of  an  astig- 
matic eye,  there  are,  in  skiascopy,  two  principal  areas  of  rever- 
sal, and  corresponding  to  the  intermediate  meridians  of  an 
astigmatic  eye,  there  are,  in  skiascopy,  intermediate  areas  of 
reversal  for  these  intermediate  meridians.  When  the  observ- 
ing eye  is  between  the  two  principal  areas  of  reversal  it  is 
necessarily  at  an  area  of  reversal  of  some  one  of  the  inter- 
mediate meridians,  and  as,  in  this  position,  other  areas  of  re- 
versal are  both  forward  and  back  of  it,  the  effects  are  confus- 
ing. A  spherical  lens  may  bring  the  observing  eye,  without 
changing  its  distance,  to  one  of  the  principal  areas  of  reversal, 
or  it  may  obtain  such  position  by  advancing  toward  or  reced- 
ing from  the  observed  eye.  It  is  important  to  find  one  of  the 
principal  areas  of  reversal  and  to  bring  it  to  the  cornea  of  the 
observing  eye,  for  then  all  the  other  areas  of  reversal,  being 
posterior  or  anterior  to  it,  will  be  posterior  or  anterior  to  the 
observing  eye.  To  ascertain  the  position  of  the  two  principal 
meridians  is  almost  the  first  step,  and  this  may  be  done  by 
developing  what  is  known  as  the  "banded"  appearance. 

THE   BANDED  APPEARANCE. 

This  is  a  display  at  the  pupil  of  the  observed  eye  as 
though  a  band  of  light,  narrower  than  the  pupil  usually,  ex- 
tended across  it.  The  direction  of  the  band  shows  the  position 


SUBJECT    DEFINED   AND    OUTLINED.  39 

of  one  of  the  principal  meridians.  The  development  of  this 
banded  appearance  in  astigmatism  occurs  quite  distinctly 
when  the  observing  eye  is  at  one  of  the  principal  areas  of  re- 
versal, but  it  may  be  made  more  striking  even  then.  To  pro- 
duce the  most  striking  banded  pupillary  display,  the  observing 
eye  must  not  only  be  at  one  of  the  principal  areas  of  reversal, 
but  the  aerial  image  at  the  cornea  should  be  made  doubly  cor- 
rect by  a  correct  focus  in  one  meridian  of  the  observed  eye,  so 
that  the  preceding  retinal  image  is  diffuse  in  but  one  merid- 
ian. An  astigmatic  eye  refracts  both  the  incident  and  emerg- 
ent pencils  unsymmetrically.  If  there  is  diffusion  in  both 
principal  meridians  at  area  3,  the  aerial  image  at  the  cornea  of 
the  observing  eye  will  be  an  exaggerated  reproduction  of  such 
image;  but  if  the  original  source  of  light,  the  lamp  f^ame  or 
luminous  area,  is  the  same  distance  from  the  mirror,  in  front 
of  it,  as  the  second  principal  area  of  reversal  is  from  the  mir- 
ror, or  cornea,  back  of  it,  one  meridian  of  the  observed  eye 
will  focus  the  luminous  area.  This  is  apparent  from  the  fact 
that  the  anterior  focus  of  one  meridian  is  at  the  same  distance 
from  the  observed  eye  as  the  luminous  area.  If  such  anterior 
focus  is,  for  instance,  -J  meter  posterior  to  the  cornea  or  i^ 
meters  from  the  observed  eye,  and  the  luminous  area  is  -} 
meter  in  front  of  the  mirror  or  i-|  meters'  by  way  of  the  mirror, 
from  the  observed  eye,  that  meridian  of  the  eye  which  focuses 
an  emergent  pencil  from  the  retina  at  a  distance  of  i^  meters 
would  also  focus  upon  the  retina  an  incident  pencil  from  i-| 
meters. 

If  in  the  above  example  we  suppose  the  horizontal  merid- 
ian of  the  observed  eye  to  be  the  weaker  meridian,  it  will  be 
the  meridian  to  produce  a  focus  of  an  emergent  pencil  at  i^ 
meters.  It  will  also  focus  upon  the  retina  a  pencil  from  i^ 
meters.  But  the  vertical  or  stronger  meridian  will  focus  the 
incident  pencils  anterior  to  the  retina  and  produce  dififusion 
in  the  vertical.  As  a  result  the  retinal  image  at  area  3  will  be 
elongated  vertically  but  correct  horizontally.  Pencils  from 
this  image  will  be  focused  in  the  vertical  meridian  at  one 
meter  or  at  the  cornea  of  the  observing  eye,  and  be  there 
transposed;  but  in  the  horizontal  meridian  the  pencils  will  not 
have  come  to  their  foci.     The  aerial  image  at  the  cornea  is 


40  SUBJECT    DEFINED   AND    OUTLINED. 

thus  elongated  horizontally.  The  emmetropic  observing  eye 
now  refracts  both  meridians  symmetrically,  but  the  pencils 
upon  which  it  acts  are  divergent  in  the  vertical  and  convergent 
in  the  horizontal.  The  observing  eye  may  get  a  nearly  correct 
focus  by  its  horizontal  meridian,  but  there  will  be  large  dif- 
fusion circles  in  the  vertical.  This  gives  an  image  elongated 
in  the  vertical  the  same  as  the  preceding  retinal  image  in  the 
observed  eye,  it  does  not  matter  whether  inverted  or  upright, 
since  it  would  be  vertical  in  either  case.  The  optician  need 
not  pause  in  his  work  to  analyze  these  effects,  but  by  remov- 
ing the  luminous  area  to  a  greater  or  less  distance  he  will 
bring  out  the  banded  appearance.  He  may  also  bring  out 
the  banded  appearance  by  approaching  or  receding  from  the 
observed  eye,  provided  he  does  not  allow  himself  to  approach 
or  recede  from  the  luminous  area  at  the  same  time,  for  that 
would  affect  all  three  intervals  at  once  when  it  is  only  desired 
to  affect  the  sum  of  intervals  i  and  2. 

In  the  case  given  the  banded  appearance  would  be  verti- 
cal and  indicate  that  the  vertical  was  one  chief  meridian. 
Now,  this  gives  the  meridian  of  greatest  power  as  the  vertical 
meridian.  A  positive  cylinder,  axis  vertical,  would  equalize 
the  meridians,  complete  the  primary  correction,  and  bring  all 
areas  of  reversal  to  the  cornea.  The  dioptric  power  of  such 
cylinder — that  is,  whether  it  should  be  -|-  .5  D.,  +  .75  D., 
+  1.5  D.,  or  of  some  other  power,  would  be  revealed  by  trial. 
There  may  be  a  -f  3  D.  spherical  lens,  however,  before  the 
eye  that  is  brought  to  the  conditions  given,  or  a  —  2D.  or 
some  other  spherical  lens.  If  the  cylinder  proves  to  be  a 
4-  I  D.,  and  there  is  a  -{-  3  D.  sph.  already  before  the  eye,  the 
primary  correction  is : 

+  3  D.  sph.  C  +  I  D-  cyl.  ax.  90°. 

But  adding  the  secondary  correction  of  —  i  D,  to  this  gives: 

4-  2  D.  sph.  C  +  I  D.  cyl.  ax.  90°. 

which  is  the  complete  correction.  But  the  spherical  correc- 
tion may  have  been  a  —  2D.  sph.  In  that  case  the  completed 
primary  correction  is: 

—  2D.  sph.  3  +  I  D.  cyl.  ax.  90°. 


SUBJECT    DEFINED    AND    OUTLINED,  41 

But  this  combination  reduces  to: 

—  I  D.  sph.  C  —  I  D.  cyl.  ax.  i8o°. 
Adding  the  secondary  correction  of  —  i  D.  to  this  we  have: 

—  2D.  sph.  C  —  I  D.  cyl.  ax.  i8o°. 
This  is  the  complete  correction  in  its  simplest  form. 

In  each  of  the  following  figures  three  common  conditions 
are  supposed  to  exist:  (i)  The  light  or  source  of  the  pencils 
is  at  a  finite  distance,  one  meter;  (2)  the  accommodation  is 
passive;  (3)  a  degree  of  astigrnatism  exists  in  each  eye. 


Incident  Pencil.— Simple  Hyperopia  Astigmatism. 


o 


C— Luminous  Area.  X>— Retinal  Figure,  enlarged. 


Emergent  Pencil. — Simple  Hyperopic  Astigmatism. 


Fig.  10  A  represents  the  refraction  of  an  incident  pencil 
of  light  by  an  eye  having  simple  hyperopic  astigmatism,  the 
potential  focus  of  the  emmetropic  meridian  being  at  F,  pos- 
terior to  the  retina,  and  that  of  the  hyperopic  meridian  being 
at  F'  posterior  to  F.  As  a  result  of  these  conditions  diffusion 
will  prevail  at  the  retina  for  all  meridians,  but  diffusion  will  be 
greatest  along  the  meridian  of  hyperopia.  An  image  of  the 
candle  flame  would  thus  be  elongated  in  the  meridian  of  hy- 
peropia, at  right  angles  to  the  meridian  of  emmetropia.     If 


42 


SUBJECT    DEFINED   AND    OUTLINED. 


the  pencil  were  from  infinity  or  the  eye  were  accommodated 
for  one  meter,  F  would  be  at  the  retina,  but  F'  would  still  be 
posterior  to  it,  and  diffusion  would  be  confined  to  the  meridian 
of  greatest  hyperopia. 

Fig-.  ID  B  represents  an  emergent  pencil  from  the  same 
eye.  The  emmetropic  meridian  neutralizes  the  pencil,  but  the 
hyperopic  meridian  is  unable  to  do  so.  If  a  positive  spherical 
lens  or  emmetropic  eye  focused  the  emergent  pencils  in  the 
emmetropic  meridian  of  the  observed  eye  it  would  be  unable 
to  focus  the  pencil  exactly  in  the  two  meridians  at  the  same 
time.  At  one  meter  the  difference  of  the  two  meridians  would 
be  reduced  by  the  evolution  of  the   waves   of  the   hyperopic 


Fig.  11. 


Incident  Pencil.— Compound  Hyperopic  Astigmatism. 


Emergent  Pencil.— Compound  Hyperopic  Astigmatism. 


meridian,  tending  to  make  them  neutral  in  all  meridians.  If 
the  astigmatism  were  one  diopter  and  the  eye  were  accommo- 
dated for  one  meter,  the  emergent  pencil  would  be  focused  by 
the  emmetropic  meridian  at  one  meter,  but  the  ametroplc 
meridian  (i  D.  hyperopic)  would  simply  neutralize  the  pencil. 
The  emergent  pencils,  in  this  case,  would  form  at  one  meter 
an  image  diffuse  in  hyperopic  meridian  but  focused  in  the 
emmetropic,  the  same  as  a  +  i  D.  cylinder,  but  the  original 
of  this  aerial  image  would  be  the  preceding  retinal  image. 

Fig.  II  A  represents  a  pencil  of  light  being  refracted  by 
an  eye  having  compound  hyperopic  astigmatism,  F'  being  the 


SUBJECT    DEFINED    AND    OUTLINED.  43 

potential  focus  of  the  meridian  of  least  hyperopia  and  F"  the 
focus  of  the  meridian  of  greatest  hyperopia.  F  represents  the 
position  of  the  focus  for  emmetropia  under  the  conditions 
named.  It  is  evident,  in  this  case,  that  diffusion  will  be  greatest 
at  the  retina  for  that  meridian  which  has  the  greatest  degree  of 
hyperopia,  and  the  image  of  the  candle  flame  will  be  corre- 
spondingly elongated  in  that  meridian.  Fig.  ii  B  represents 
an  emergent  pencil  for  the  same  eye.  If  the  eye  is  one  diopter 
hyperopic  in  the  horizontal  and  two  diopters  hyperopic  in  the 
vertical,  a  +  i  D.  lens  would  neutralize  the  emergent  pencil 
in  the  horizontal  and  place  F'  at  F  for  the  incident  pencil.  A 
+  2  D.  lens  would  place  F'  at  the  retina  and  F"  at  F,  making 
the  eye  artificially  myopic  one  diopter  in  the  horizontal  and 
emmetropic  in  the  vertical.  With  such  +  2  D.  lens  diffusion 
would  be  confined  to  the  emmetropic  vertical  meridian,  for  the 
incident  pencil  would  be  focused  by  the  myopic  horizontal 
meridian.  But  the  emergent  pencils  from  the  retinal  image 
would  be  focused  at  one  meter  by  the  myopic  horizontal 
meridian,  and  diffuse  in  the  vertical,  forming  an  aerial  image 
doubly  diffuse  in  the  vertical,  for  it  would  be  diffuse  in  the  ver- 
tical if  it  were  a  direct  reproduction  of  the  retinal  image,  and 
diffusion  would  be  increased  in  the  vertical  by  the  incapacity 
of  that  meridian  to  focus  the  emergent'pencils.  With  a  +  3  D. 
lens  the  horizontal  meridian  would  become  2  D.  myopic,  the 
vertical  i  D.  myopic.  The  incident  pencils  would  be  focused 
upon  the  retina  by  the  vertical  meridian,  but  forward  of  the 
retina  by  the  horizontal  meridian,  resulting  in  diffusion,  in  the 
horizontal,  at  the  retina.  The  aerial  display  at  -J  meter  would 
be  diffuse  in  the  vertical  but  focused  by  the  horizontal,  but  as 
such  aerial  image  is  an  image  of  the  preceding  retinal  image, 
which  is  diffuse  in  the  horizontal,  there  would  be  diffusion  in 
both  meridians.  At  one  meter,  however,  the  vertical  meridian 
would  focus  and  the  horizontal  become  diffuse,  producing 
double  diffusion  in  the  horizontal. 

Fig.  12  A  represents  an  incident  pencil  being  refracted 
by  an  eye  having  simple  myopic  astigmatism  of  one  diop- 
ter. The  incident  pencil  is  focused  by  the  myopic  meridian 
at  the  retina,  the  emmetropic  meridian  focusing  at  F  posterior 
to  the  retina.    Tlie  one  diopter  of  work  given  all  meridians  of 


44 


SUniECT    DEFINED    AND    OUTLINED. 


the  eye  by  the  nearness  of  the  object  is  performed  by  the 
myopic  meridian;  but  the  emmetropic  meridian  is  unable  to 
focus  at  the  retina  without  the  use  of  one  dioptry  of  accommo- 
dation. Diffusion  in  the  emmetropic  meridian  results.  Fig. 
12  B  represents  an  emergent  pencil  being  refracted  by  such  eye. 
The  emmetropic  meridian  neutralizes  the  pencil  merely,  but 
the  myopic  meridian  focuses  it  at  one  meter.  If  the  observed 
•eye  is  one  diopter  myopic  in  the  vertical  and  emmetropic  in 
the  horizontal,  the  retinal  image  produced  by  the  incident  pen- 
cils will  be  diffuse  in  the  horizontal,  forming  a  figure  elongated 
horizontally  because  of  diffusion  in  the  horizontal.    Emergent 


Fig.  12 


Incident  Pencil.— Simple  Myopic  Astigmatism  —1  Diopter 


Emergent  Pencil.— Simple  Myopic  Astigmatism.— 1  Diopter. 


pencils  proceeding  from  this  figure  will  be  focused  at  one 
meter  by  the  vertical  meridian,  forming  an  aerial  image  doubly 
elongated  in  the  horizontal — elongated  by  the  original  retinal 
image,  and  by  diffusion  in  the  horizontal  for  emergent  pencils. 
But  if  an  observing  emmetropic  eye  be  at  one  meter  it  will 
focus  the  pencils  in  the  horizontal  but  not  in  the  vertical,  pro- 
ducing, at  the  retina  of  the  observing  eye,  diffusion  in  the  verti- 
cal. The  eye  has  no  capacity  to  refocus  pencils  already 
focused  at  or  within  its  dioptric  media  by  some  preceding 
lens  action.  But  horizontal  diffusion  at  the  retina  of  the 
observed  eye  will  not  be  overcome  by  vertical  diffusion  at  the 
retina  of  the  observing  eye.  There  will  be,  therefore,  in  this 
case,  diffusion  in  both  meridians. 


SUBJECT    DEFINED    AND    OUTLINED. 


45 


Fig.  13  A  represents  the  refraction  of  an  incident  pencil 
■of  light  by  an  eye  having  compound  myopic   astigmatism, 


Fig.  13. 


Incident  Pencil.— Compound  Myopic  Astigmatism. 


Emergent  Pencil.— Compound  Myopic  Astigmatism. 

myopia  being  of  one  diopter  in  the  least  myopic  meridian,  and 
more  than  one  diopter  in  the  opposite  meridian.  The  incident 
pencil  is  focused  upon  the  retina  by  the  least  myopic  meridian, 
but  forward  of  it  by  the  other  chief  meridian.  Fig.  13  B  rep- 
resents a  pencil  of  light  emerging  from  the  above  eye.  The 
emergent  pencil  is  focused  at  one  meter  by  the  least  myopic 
meridian,  but  nearer  than  one  meter  by  the  meridian  of  greatest 
myopia.  If  the  astigmatic  element  is  one  diopter,  a  —  i  D.  sph. 
would  convert  the  case  into  one  of  simple  myopic  astigmatism 
of  one  diopter. 

Fig.  14. 


Incident  Pencil.— Mixed  Astigmatism. 


Emergent  Pencil.— Mixed  Astigmatism. 


Fig.   14  A  represents  an  incident  pencil  of  light  being 
refracted  by  an  eye  having  mixed  astigmatism.     The  degree 


46  SUBJECT    DEFINED   AND    OUTLINED. 

of  myopia  shown  is  more  than  one  diopter,  while  the  degree  of 
hyperopia  is  not  indicated.  Myopia  is  shown  to  be  in  excess 
of  one  diopter  by  the  position  of  the  focus  forward  of  the  retina 
in  Fig.  14  A.  But  it  is  also  shown  by  the  position  of  the  focus 
of  the  emergent  pencil  within  one  meter  of  the  eye. 

The  foregoing  constitutes  the  elementary  principles  of  the 
practice  of  skiascopy.  But  the  only  way  to  understand  a  sys- 
tem is  to  know  the  system  all  through.  The  following  chapters 
will  be  devoted  to  evolving  the  principles,  describing  the 
methods  and  means,  developing  further  possibilities  of  the 
test  and  grounding  the  reader  upon  the  general  principles  of 
optics  as  related  to  this  interesting  method  of  examination. 


CHAPTER  11. 


GENERAL  OPTICAL  PRINCIPLES.  NOTATION  OF  LIGHT  AND 
OF  CURVED  SURFACES.  DYNAMIC  PROPERTIES  OF  A  WAVE 
OF  LIGHT. 


BEFORE  proceeding  further  it  seems  necessary  to  make  a 
little  excursion  into  the  field  of  general  optics,  and  to 
prepare  the  reader  to  understand  the  language  it  will  be  neces- 
sary to  employ  in  the  succeeding  chapters  of  this  book,  for  it 
will  be  necessary  to  use  terms  not  at  present  in  general  optical 
text-books  and  writings.  This  new  optical  language  grows 
out  of  the  analysis  of  the  force  with  which  optics  deals — the 
force  of  light. 

We  will  start  with  the  pencil  of  light.  Most  opticians 
would  at  once  consider  that  they  comprehend  fully  what  a 
pencil  of  light  is,  and  undoubtedly  they  do,  but  an  analysis  of 
this  primary  factor  in  all  optical  phenomena  will  show  that 
there  is  a  chance  to  get  a  better  idea  of  something  we  are  in 
the  habit  of  considering  every  day.  A  pencil  uf  light  is  com- 
posite. Of  what  is  it  composed?  We  do  not  refer  now  to 
its  chromatic  elements  but  to  its  simple  optical  elements. 
Probably  two-thirds  of  all  the  opticians  would  say  that  a  pen- 
cil of  light  is  composed  of  rays  of  light,  or  that  a  pencil  of  light 
is,  as  some  writers  express  it,  a  "bundle  of  rays." 

We  do  not  consider  this  answer  to  be  satisfactory,  and 
will  show  why.  What  is  a  ray  of  light?  A  ray  of  light  may 
be  considered  as  a  mere  mathematical  line,  or  as  a  physical 
part  of  a  pencil  of  light.  Of  course  in  the  former  light  it  is 
not  a  part  of  the  pencil  any  more  than  the  equator  is  a  part  of 
the  earth,  but  in  the  latter  aspect  it  is  a  minute  fractional  part 
of  a  pencil  of  light — so  minute  that,  for  all  practical  purposes, 
it  may  be  regarded  as  a  line.  To  say  then  that  a  pencil  of 
light  is  composed  of  rays  of  light,  is  to  say  that  it  is  composed 


48  GENERAL    OPTICAL    PRINCIPLES. 

of  fractional  parts.  That,  surely,  is  not  a  good  answer,  for 
every  unit  is,  as  a  matter  of  course,  composed  of  fractional 
parts. 

If  you  were  asked,  "Of  what  is  an  apple  composed?" 
would  it  be  a  good  answer  to  say,  "An  apple  is  composed  of 
four  quarters  of  an  apple,  or  of  quarters,  or  hundredths,  or 
thousandths,  or  millionths?"  Certainly  not.  That  would  be 
simply  avoiding  the  question.  But  if  you  should  say  of  its 
skin,  its  pulp  and  core  with  seeds,  the  answer  would  be  more 
satisfactory.  Within  the  apple  there  are  seeds.  A  seed  may 
be  of  exactly  one-hundredth  of  the  bulk  of  the  apple  or  one- 
fiftieth  of  its  weight,  but  the  seed  is  an  elementary  part  of  the 
apple  aside  from  any  consideration  of  this  kind.  The  seed  is 
as  much  a  unit  as  the  apple,  but  it  is  a  different  kind  of  unit. 
A  pencil  of  light  is  composite  in  the  same  way.  It  is  com- 
posed of  more  elementary  units,  not  rays,  but  something  else. 

Light  is  propagated  in  a  homogenous  medium  in  great 
spherical  waves.  At  starting  these  spheres  are  very  minute, 
but  they  enlarge  very  rapidly.  Light  is  generated  at  points, 
and  each  luminous  point  is  the  center  of  a  whole  series  of 
spherical  waves.  But  by  the  reflection  of  rough  surfaces, 
although  the  preceding  order  of  the  waves  is  broken,  new 
spherical  waves,  composed  of  the  impulses  of  the  dissociated 
incident  waves,  are  formed.  So,  whether  from  a  luminous 
point  or  an  opaque  point  of  reflection,  these  series  of  waves  of 
light  extend  out  into  space.  A  pencil  of  light  is  a  definite 
conic  section  of  such  a  sphere.  It  is  conjjDosed  of  a  fractional 
part  of  each  wave  from  the  point  of  starting  outward.  There 
is  a  definite  distance  from  crest  to  crest  between  these  waves, 
but  that  is  of  little  optical  importance,  for  the  crests  and  hol- 
lows, or  extreme  positions  of  molecular  motion,  are  no  more 
important  than  the  slopes. 

The  principal  element  of  optical  importance  in  the  waves 
is  their  degree  of  curvature.  The  degree  of  curvature  is  great- 
est at  and  near  the  point  of  starting  or  center  of  curvature. 
The  curvature  of  the  waves  decreases  with  their  distance  from 
this  center  of  curvature,  and  it  is  with  respect  to  curvature  that 
a  notation  or  nomenclature  is  of  optical  value.  The  author 
has  improvised  such  a  notation  by  designating  the  curvature 


GENERAL    OPTICAL    PRINCIPLES. 


49 


of  a  wave  one  meter  from  its  center  of  curvature,  as  one  curv- 
ometer,  or  i  Cm.  The  curvature  of  a  wave  ^  meter  from  its 
center  is  then  2  Cm.,  and  2  meters  from  its  center  of  curvature 


Fig.  15. 


is  ^  Cm.  In  other  words,  the  curvature  of  a  wave  is  inversely 
proportional  to  its  distance  in  meters  from  the  center  of  curv- 
ature. A  wave  8  in.  from  such  center  has  then  a  curvature 
of  40/8  =  5  Cm.  Fig-.  15  illustrates  this  notation,  showing  the 
regular  decrease  of  curvature  as  the  wave  advances  into  space. 


Fig.  16. 


But  with  the  evolution  of  decreased  curvature  there  is  a 
coordinate  and  compensating  expansion  of  the  wave.  It 
evolves,  as  it  advances,  increased  extent  in  direct  proportion 
to  its  radii.  Measured  by  the  arc  that  subtends  a  given  angle, 
or  by  the  sine  of  such  angle,  the  extent  of  the  wave  is  directly 
proportional  to  the  radii,  and  therefore  the  curvature  is  in- 
versely proportional  to  the  sines  of  a  given  central  angle.  In 
Fig.  16  let  M  be  the  center  of  curvature  of  a  wave,  and  G  E  and 


50  GENERAL    OPTICAL    PRINCIPLES. 

D  K  represent  the  positions  of  a  wave,  respectively  one  and  two 
intervals  from  M,  then  will  sine  F  E  =  ^  sine  P  K.  The  truth 
of  the  above  is  established  by  the  proposition  that  "a  line 
parallel  to  the  base  line  of  a  triangle  divides  the  other  sides 
proportionally,  and  is  itself  in  the  same  ratio  to  the  base  line." 
But  F  G  is  also  ^  oi  P  D,  for,  since: 

(i)  M  G:M  D::M  F:M  P,  then 

(2)  M  G:M  F:  \MD\MP,  and 

(3)  M  G  —  M  F:M  G::M  D  —  M  P:MD,  or 

(4)  FGiM  G::PD:M  D,  from  which 

(5)  FG:PD:  :MG:MD, 

and  F  G  =  ^  P  D.  The  same  principle  would  apply  to  a  wave 
at  any  distance  from  M,  if  evolved  in  a  homogeneous  medium, 
for  a  given  angle  at  the  center.  But  the  principle  would  apply 
for  any  angle  at  the  center,  although  for  a  different  angle  than 
m  the  case  would  be  a  different  one,  and  vary  the  sines  pro- 
portionately. For  instance,  if  a  wave  of  light  is  generated  at 
any  other  point  on  M  D,  or  M  D  extended,  as  at  H,  and  the 
instant  the  wave  from  H  reaches  L,  the  same  distance  from  K 
as  M,  a  wave  starts  from  M,  both  waves  will  reach  K  at  the 
same  instant.  But  their  curvature  at  K  will  not  be  the  same, 
but  inversely  proportional  to  H  K  and  M  K.  If  the  wave 
started  from  M  at  the  instant  the  wave  from  H  reached  M, 
both  would  reach  P  at  the  same  instant,  but  their  curvature  at 
P  would  be  inversely  proportional  to  H  P  and  M  P.  With 
both  waves  at  K,  P  K  will  be  the  common  sine  of  both  waves 
or  both  angles,  m  and  n,  although  the  sine  of  each  will  pertain 
to  the  different  circles.  Now  if  through  K  a  line  is  drawn 
parallel  to  H  D,  and,  with  K  as  a  center  and  M  K  as  a.  radius, 
an  arc  is  struck  across  the  two  parallels,  and  the  sines,  M  S 
and  L  T  are  drawn,  the  latter  will  be  the  sines  of  the  two  angles 
in  the  same  circle,  for  angle  n  =  angle  n  and  n'  +  0  =  m. 
Now,  these  two  sines  are  inversely  proportional  to  the  radii  of 
the  two  circles.     That  is: 

(i)  Sine  L  T:  sine  M  S::M  K:H  K. 
For  L  T  K  and  H  K  P  are  similar  triangles  because  mutually 
equiangular,  and  corresponding  sides  are  proportional,  hence: 

(2)  LT:P  K::LK:H  K. 


GENERAL    OPTICAL    PRINCIPLES. 


51 


But,  SiS  P  K  =  M  S  and  L  K  =  M  K,  this  proportion  (2) 
reduces  to  (i)  by  the  substitution  of  these  equivalent  terms, 
and  L  T,  the  sine  of  angle  n  of  the  large  circle,  is  to  P  K,  the 
sine  of  angle  ni  of  the  small  circle,  as  the  radius  M  K  of  the 
small  circle  is  to  radius  H  K  oi  the  large  circle.  Hence  of  two 
unequal  circles,  angles  at  the  center  of  which  are  subtended 
by  a  common  sine,  the  sines  of  such  angles  in  equal  circles  are 
inversely  proportional  to  the  radii  of  the  circles.  But  as  the 
curvature  of  the  waves  are  also  inversely  proportional  to 
radii,  it  follows  that  such  curvature  is  directly  proportional  to 
the  sines  of  the  two  angles  in  equal  circles.  That  is,  the 
curvature  of  the  wave  from  M  at  K  is  to  the  curvature  of  the 
wave  from  H  at  K,  as  P  K  is  to  L  T. 

For  a  very  minute  pencil  of  light  at  P — one  so  minute 
that  a  representation  of  it  by  a  drawing  would  be  practically 
impossible,  would  evidently  be  governed  by  the  same  rule. 
But  in  such  a  pencil  L  would  be  so  near  M  that  both  might 
be  considered  as  one.  Sine  L  T  would  thus  reduce  to  zero, 
but  P  K  would  also  become  zero  under  this  hypothesis.  For 
the  most  minute  distance  imaginable  separating  L  and  M,  the 
ratio  of  sines  would  be  maintained,  however,  and  would  be 
practically  as  M  P  io  H  P,  and  the  two  waves  at  P,  one  from 
H,  the  other  from  M,  would  be  to  each  other,  in  curvature,  in 
inverse  ratio  of  M  P  to  H  P,  but  at  D  in  inverse  ratio  of  M  D 
to  H  D. 


In  Fig.  17  we  have  represented  a  pencil  of  light  being 
acted  upon  by  a  bi-convex  lens.  The  lens  focuses  the  pencil 
from  C  at  C.  Now,  it  will  be  noticed  that  the  pencil  is  com- 
posed of  three  parts  or  sections:  (i)  the  section  anterior  to  the 

4 


52  GENERAL    OPTICAL    PRINCIPLES. 

lens;  (2)  the  section  within  the  lens,  and  (3)  the  section  poste- 
rior to  the  lens.  But  at  each  surface  the  wave  is  partly  within 
and  partly  without  the  lens,  during  the  time  of  its  entrance 
into  or  emergence  from  the  lens.  The  figure  represents  the 
lens  as  exactly  neutralizing  or  taking  all  curvature  out  of  the 
incident  wave  at  the  anterior  surface,  and  converting  it  into  a 
concave  wave  at  the  second  surface.  A  lens  may  or  may  not 
have  this  action.  If  this  pencil  had  started  from  a  point  farther 
away  than  C,  the  first  surface  alone  would  have  converted  the 
waves  into  concave  waves  (Fig.  18),  but  if  C  were  nearer  the 

Fig.  18. 


lens,  refraction  at  the  first  surface  would  have  left  the 
waves  convex,  though  less  so  than  before.  But  if  refraction 
at  the  first  surface  were  different  than  it  is  the  results  at  the 
second  surface  would  also  be  different.  Perhaps  the  focus  C 
would  be  farther  away,  or  perhaps  both  surfaces  of  the  lens 
would  barely  neutralize  the  pencil  and  make  the  emergent 
waves  plane. 

The  effects  of  a  lens  upon  a  pencil  of  light  depends,  then, 
upon  the  curvature  of  the  waves  of  which  the  pencil  is  com- 
posed as  well  as  upon  the  power  of  the  lens,  and  the  curvature 
of  the  waves  upon  which  a  lens  acts  depends  upon  the  nearness 
of  the  center  of  curvature.  What  is  the  force  by  which  a  lens 
changes  the  curvature  of  these  waves  of  light?  It  is  the  force 
of  resistance.  The  glass  of  which  the  lens  is  composed  resists 
the  propagation  of  the  waves  in  it.  As  this  increased  resistance 
is  applied,  at  the  first  surface,  to  that  point  in  the  wave  which 
reaches  it  first,  it  is  delayed  while  all  other  points  in  the  wave 
are  gaining  upon  it.  But  at  the  second  surface  the  point  in  the 
wave  first  to  enter  the  glass,  may  be,  by  the  shape  of  the  lens, 
the  last  to  be  released  from  its  resisting. influence.    As  a  result 


GENERAL    OPTICAL    PRINCIPLES.  53 

refraction  at  the  second  surface  gives  the  other  points  of  a  wave 
still  further  advantage,  and  the  w^ave  is  transposed,  or  changed, 
by  the  lens  from  convex  to  concave. 

In  this  transposition  it  will  be  noted  that  the  center  of 
curvature  of  the  waves  of  the  pencil  is  sent  to  infinity  on  one 
side  of  the  lens  by  refraction  at  the  first  surface,  but  that  it  is 
brought  back  to  a  finite  position  on  the  other  side  of  the  lens 
by  refraction  at  the  second  surface.  These  are  important 
optical  effects.  The  mere  deflection  of  rays  by  the  lens,  as 
shown  by  the  change  of  direction  of  the  lines,  does  not  give  a 
clear  conception  of  this  optical  transformation  of  the  pencil  or 
of  the  waves  of  the  pencil.  Rays  of  light  are  of  dififerent  pen- 
cils and  are  confused  with  one  another,  but  when  the  attention 
is  directed  to  the  waves  of  which  the  pencil  is  composed  no 
such  confusion  can  arise.  The  bending  of  the  rays  is  a  conse- 
quence of  the  modification  of  the  waves.  The  waves  are  the 
physical  elements  upon  which  the  lens  acts. 

Now  the  curvature  of  the  waves  anterior  to  the  lens  (Fig. 
17)  is  convex,  the  curvature  of  the.  waves  within  the  lens  is 
neutral,  and  the  curvature  of  the  waves  posterior  to  the  lens  is 
concave.  These  are  different  classes  of  waves,  although  these 
waves  are  all  of  one  pencil  of  light.  ^The  curvature  of  the 
waves  posterior  to  the  lens  is  determined  by  their  position  with 
reference  to  C  not  C.  If  a  wave  is  one  meter  from  C  and  con- 
cave, its  curvature  is  i  Cm.  as  before,  but  our  nomenclature 
should  distinguish  the  kind  or  class  of  waves  as  well  as  their 
degree  of  curvature.  For  this  purpose  we  call  all  convex 
waves — the  waves  as  they  are  generated,  or  natural  waves — 
positive  or  plus  waves;  while  waves  that  are  optically  trans- 
posed into  concave  waves  are  negative  or  minus  waves. 
Waves  having  no  curvature  are  simply  neutral  waves.  A  wave 
then  of  +  5  Cm.  is  a  convex  wave  one-fifth  of  a  meter  or  eight 
inches  from  the  point  from  which  it  started;  and  a  —  8  Cm. 
wave  is  a  concave  wave  one-eighth  of  a  meter,  or  five  inches 
from  its  new  center  of  curvature.  Statically  considered  a  +  5 
Cm.  wave  and  a  —  5  Cm.  are  exactly  alike.  It  is  true  one  is 
convex  and  the  other  is  concave,  but  what  is  the  difference 
between  convex  and  concave  except  in  the  point  of  view? 
Whatever  is  convex  on  one  side  is  concave  on  the  other. 


54  GENERAL    OPTICAL    PRINCIPLES. 

DYNAMIC  PROPERTIES. 

But  dynamically  considered  there  are  great  differences 
between  these  positive  and  negative  waves.  Let  us  note  some 
of  their  important  differences: 

1.  Positive  waves  are  natural — the  only  waves  that  nature 
spontaneously  generates.  Negative  waves  are  artificial  or 
optical. 

2.  Positive  waves  start  from  their  centers  of  curvature  and 
proceed  outward  into  space.  Negative  waves  are  on  their  way 
to  their  centers  of  curvature. 

3.  Positive  waves  grow  weaker  in  curvature  as  they 
advance,  and  at  infinity  their  curvature  is  o.  Negative  waves 
grow  stronger  or  increase  in  curvature  as  they  advance  and, 
at  their  center  of  curvature,  their  curvature  is  infinite. 

4.  A  positive  wave  remains  a  positive  wave  as  long  as  it 
has  its  freedom  of  action.  Negative  waves  are  transposed  into 
positive  waves  at  their  center  of  curvature  by  natural  evolution. 

5.  The  center  of  curvature  of  positive  waves  is  a  luminous 
point,  or  a  point  of  reflection  from  which  the  series  starts. 
The  center  of  curvature  of  a  series  of  concave  waves  is  a  focus. 

These  points  give  a  comprehension  of  the  real  differences 
between  these  two  opposite  classes  of  waves.  Now,  it  must  be 
borne  in  mind  that  transposition  of  a  pencil  of  light  does  not 
bring  out  a  new  and  different  pencil.  The  pencil  of  concave 
waves  is  the  pencil  of  convex  waves  transposed.  The  series  of 
waves  is  the  same  series.  There  is  no  loss  of  identity  by  trans- 
position, any  more  than  there  is  the  loss  of  identity  of  a  coat 
by  being  turned  inside  out.  The  focus  of  the  negative  pencil 
is  the  center  of  curvature  of  the  positive  pencil,  located  in  a 
new  place.  Whatever  the  molecular  activity  at  the  center  of 
curvature  of  a  positive  pencil  of  light  that  activity  is  repro- 
duced or  duplicated  at  the  focus,  or  new  center  of  curvature, 
to  which  the  waves  of  the  pencil  converge.  When  the  foci 
of  numberless  pencils  are  thus  brought  near  to  each  other, 
and  a  screen  or  receiving  surface  is  so  placed  as  to  react  upon 
the  pencils  at  that  critical  point  in  their  career,  an  image,  the 


GENERAL    OPTICAL    PRINCIPLES.  55 

exact  counterpart  of  the  object  or  luminous  area,  except  that 
it  is  inverted,  and  may  be  of  different  size,  is  displayed  upon 
the  screen.  To  see  this  image  thus  displayed  general  light 
must  be  excluded  from  the  screen,  but  the  image  is  on  the 
screen  whether  general  light  is  excluded  or  not.  The  screen, 
even,  is  unnecessary,  except  for  the  display  of  the  image,  for 
the  image  is  wherever  the  foci  of  the  pencils  are  thus  grouped, 
no  matter  whether  displayed  or  not.  Such  an  image  is  a  true 
image,  because  it  is  an  image  intermediate  to  and  lying 
between  the  object  and  the  eye.  A  virtual  image  is  the  pro- 
jection of  a  real  image  upon  the  retina  to  some  other  position 
than  that  occupied  by  the  object.  The  object  itself,  considered 
visually,  is  nothing  more  than  the  projection  of  a  retinal  image. 
.  This  gives  us  a  comprehension  of  the  composite  pencil  of 
light  that  no  study  of  the  rays  as  such  gives.  Perhaps  the 
most  wonderful  feature  of  these  ethereal  waves  is  their  non- 
interference. Each  series  acts  across  a  space  where  thousands 
of  other  series  are  playing  as  freely  as  if  it  had  an  exclusive 
franchise  to  the  space.  Millions  of  pencils  and  series  of 
waves  pass  simultaneously  through  a  lens,  and  in  as  many 
directions,  without  interfering  with  one  another,  each  pencil 
being  focused,  if  the  lens  is  capable  of  transposing  it,  in  or  at 
its  own  individual  point.  But  pencils  from  points  in  the  same 
straight  line,  axial  to  the  lens,  are  acted  upon  by  the  lens  simul- 
taneously. The  foci  of  the  pencils  from  the  near  points  are 
far  away,  and  the  foci  of  the  pencils  from  far  away  points  are 
near  the  lens.  The  foci  of  such  a  system  of  pencils  form  a 
straight  line  on  the  posterior  side  of  the  lens,  the  same  as  the 
points  of  origin  form  a  line  on  the  anterior  side. 

Pencils  that  fall  upon  a  lens  from  an  oblique  direction  are 
deflected  or  turned  to  one  side,  apparently  while  in  the  lens. 
Such  a  pencil  is  merely  a  minor  pencil  of  some  larger  major 
pencil.  The  minor  pencils  of  a  pencil  whose  center  is  upon  the 
principal  axis  of  the  lens  are  deflected  by  the  lens  in  the  same 
way.  The  action  of  the  lens  is  symmetrical,  but  by  reason  of 
its  position  an  outer  minor  pencil  only  of  the  larger  major  pen- 
cil reaches  it.  The  iris  of  the  eye  excludes  from  the  crystalline 
lens  all  except  a  minor  pencil  from  one  side  of  the  major  pencil, 
and  deflection  at  both  surfaces  is  toward  the  axial  ray — that 


56  GENERAL    OPTICAL    PRINCIPLES. 

point  in  the  wave  which  is,  or  would  be  if  given  access  to  the 
lens,  refracted  twice,  equally,  and  in  opposite  directions,  at  its 
two  surfaces. 

OPTICAL  MODIFICATIONS. 

All  optical  effects  or  phenomena  are  due  to  the  modifica- 
tion of  waves  of  light,  and  there  are  two  directions  in  which 
such  modification  may  be  made.  Referring  to  Fig.  17,  the 
modification  of  the  waves  by  the  first  surface  of  the  lens  is 
toward  or  in  the  direction  of  neutralization,  but  modification  at 
the  second  surface  is  toward  or  in  a  direction  away  from 
neutralization.  Both  of  these  refractions  are,  however,  of  the 
same  class  and  in  the  same  direction,  for  each  neutralizes  posi- 
tive curvature.  The  refraction  of  the  first  surface  takes  away 
all  positive  curvature,  but  the  refraction  of  the  second  surface 
makes  the  waves  concavfe  or  negative — still  farther  removed 
from  positive  curvature.  This  direction  of  optical  modification 
is  the  positive  direction,  or  positive  refraction.  Positive  refrac- 
tion, or  positive  optical  modification  of  waves  of  light,  is  modi- 
fication tending  to  neutralize  positive  or  convex  curvature  of 
the  waves.  Negative  refraction  or  modification  is  the  opposite 
of  this,  for  it  tends  to  neutralize  the  curvature  of  negative 
Waves  but  augments  the  curvature  of  positive  waves.  A  surface 
of  resistance  may  be  neutral  in  refractive  effect,  even  though 
highly  convex  or  concave.  It  is  neutral  when  the  waves  of 
light  that  fall  upon  it  are  in  curvature  complementary  to  it — 
that  is,  when  their  curvature  conforms  to  the  curvature  of  the 
surface  upon  which  they  fall,  one  being  concave  and  the  other 
convex,  and  both  of  the  same  curvature.  Such  neutrality  is 
rare,  except  for  plane  surfaces  and  neutral  waves. 

But  neutral  refraction  or  optical  modification,  as  above 
explained,  is  confined,  when  it  occurs,  to  a  single  surface  usu- 
ally. In  any  of  the  forms  of  lenses  neutral  refraction  could 
occur  at  but  one  of  the  surfaces,  and  then  absolutely  but  for 
one  series  of  waves.  A  plane  surface  of  glass  is  not  necessarily 
neutral,  except  for  plane  waves  that  conform  with  it,  but  the 
refractions  at  the  opposite  surfaces,  when  parallel,  neutralize 
each  other.  A  surface,  ordinarily  positive  in  its  refractive 
effects,  may  be  negative  upon  waves  of  light  having  a  cor- 
responding curvature,  but  of  a  greater,  degree  of  curvature 


GENERAL    OPTICAL    PRINCIPLES.  57 

than  it  has,  but  the  efficacy  of  lenses,  or  their  refractive  power, 
is  the  sum  of  effects  at  the  two  surfaces,  not  the  different 
effects  at  either,  which  vary  constantly. 

OPTICAL  INSTRUMENTS. 

Optical  instruments — that  is,  primary  optical  instruments, 
consist  essentially  of  lenses,  mirrors  and  prisms.  Under  the 
term  lenses,  cylindrical  surfaces,  and  possibly  prisms,  may  be 
included,  leaving  but  lenses  and  mirrors.  A  positive  optical 
instrument  is  one  that  produces  a  positive  effect  or  positive 
effects  upon  the  waves  of  light  upon  which  it  acts — that  is,  it 
modifies  the  waves  in  a  positive  direction  as  explained  above. 
A  negative  instrument  modifies  the  waves  in  a  negative 
direction.  To  express  the  power  of  a  lens  we  have  the 
unit,  one  diopter.  This  unit  is  usually  defined  as  that  power 
in  a  lens  which  enables  it  to  focus  parallel  rays  of  light 
at  one  meter.  This  is  a  narrow  definition.  The  diopter  is 
really  a  unit  of  work.  It  expresses  the  work  performed  by  a 
lens,  or  by  any  optical  instrument — lens  or  mirror.  What  is 
the  work  which  it  does?  It  neutralizes  or  augments  the  curva- 
ture of  waves  of  light  one  curvometer.  A  +  i  D.  lens,  acting 
upon  +  5  Cm.  waves,  neutralizes  one  curvometer,  or  makes 
them  -f  4  Cm.  in  curvature.  If  a  +  5  D.  lens  acts  upon  +  5  Cm. 
waves  it  neutralizes  all  curvature,  and  makes  the  waves  plane 
or  neutral.  If  a  +  5  D.  lens  acts  upon  +  i  Cm.  waves,  it  trans- 
poses them  into  —  4  Cm.  waves.  If  it  acts  upon  neutral  waves 
it  makes  them  —  5  Cm.  In  any  and  all  cases  the  lens  does  five 
diopters  of  positive  work.  Part  of  this  work  may  be  the 
neutralization  of  the  positive  quality  in  the  waves  upon  which 
it  acts,  and  the  other  part  be  in  imparting  the  negative  quality 
to  them;  or  all  of  its  power  may  be  devoted  to  neutralization 
of  the  positive  quality,  and  it  may  be  insufficient  in  power  for 
that. 

A  positive  lens  does  positive  work  to  the  extent  of  its 
power.  It  exhausts  its  power  upon  the  pencils  upon  which  it 
acts.  Its  work  and  the  power  of  the  lens  are  equal.  We  may 
consider  the  work  performed  by  the  lens  as  composed  of  two 
parts — that    part    previous    to    neutralization    and    that    part 


58  GENERAL    OPTICAL    PRINCIPLES. 

subsequent  to  neutralization.  We  may  consider  these  two 
parts  as  pertaining-  to  the  two  sides  (not  surfaces)  of  the  lens. 
For  instance,  if  a  +  8  D.  lens  acts  upon  +  3  Cm.  waves,  its 
anterior  work  is  +  3  D.,  and  its  posterior  work  is  +  5  D.  The 
sum  of  its  anterior  work  and  posterior  work  is  +  3  D.  +  5 
D.  =  +  8  D.  But  this  is  necessarily  equal  to  the  algebraic  dif- 
ference of  the  curvometers  anterior  and  posterior  to  the  lens. 
That  is  the  algebraic  difference  of 

+  3  Cm. 

—  5  Cm. 


+  8  Cm. 

The  lens  will  neutralize  a  series  of  +  8  Cm.  waves,  or  if  it  acts 
upon  neutral  waves  it  will  focus  them  at  40/8  =  5  inches. 
What  the  posterior  work  required  of  a  lens  may  be  depends 
upon  its  anterior  work  and  whether  that  exhausts  the  power 
of  the  lens  or  not.  If  it  does  exhaust  it,  it  does  no  posterior 
work.  If  a  +  8  D.  lens  has  +  10  D.  of  work  anterior  to  it,  it 
will  not  be  able  to  perform  it  all.  It  will,  however,  exhaust 
its  power  upon  the  work.  As  it  acts  upon  +10  Cm.  waves  it 
will  reduce  their  curvature  8  Cm.,  and  its  work  will  be  8  D., 
although  it  leaves  2  Cm.  of  positive  curvature  in  the  waves. 
Their  algebraic  difiference 

(a)  +  10  Cm. 

(c)  +     2  Cm. 


(b)  +    8  Cm. 

is  still  expressive  of  the  efficacy  of  the  lens,  its  capacity  to 
neutralize  +  8  Cm.  waves.  We  may  assume  that  that  is  its 
capacity,  and  obtain  the  curvature  of  the  emergent  waves  by 
subtracting  its  effect  upon  the  neutral  or  plane  waves  from  the 
given  waves,  thus : 

(a)  +  10  Cm. 

(b)  +    8  Cm. 


(c)  +     2  Cm, 

The  curvature  of  the  incident  waves  (a)  is  the  sum  of  the  curva- 
ture of  the  emergent  waves  (c)  and  the  neutralizing  power  of 
the  lens  (b). 


GENERAL    OPTICAL    PRINCIPLES.  59 

Negative  lenses  come  under  the  same  principles,  although 
they  act  in  an  opposite  direction.  A  —  2D.  lens  does  two 
diopters  of  negative  work.  If  it  acts  upon  +  3  Cm,  waves,  it 
converts  them  into  +  5  Cm.  waves.  Here  the  algebraic  differ- 
ence of  curvature  equals  the  power  of  the  lens.    That  is: 

+  3  Cm. 

+  5  Cm. 


2  Cm. 


The  lens  will  therefore  neutralize  —  2  Cm.  waves,  or 
reduce  the  curvature  of  —  5  Cm.  waves  to  —  3  Cm. 

The  diopter  is  a  unit  of  work.  We  see  no  reason  why  it 
may  not  be  applied  to  the  action,  or  capacity  of  action,  of  a 
mirror,  as  well  as  to  the  capacity  of  action  or  power  of  a  lens. 
There  is  no  difference  in  the  work  they  do — only  a  difference 
in  the  means  of  doing  it.  We  have  engines  of  50  horse-power, 
because  they  perform  50  units  of  work,  each  of  which  is  one 
horse-power.  Why  not  mirrors  of  3  diopters,  if  they  per- 
form 3  of  the  units  of  work  performed  by  a  lens  of  +  i  D.?  It 
does  not  matter  so  much  what  the  derivation  of  the  word  is. 
Our  scientific  language  is  full  of  departures  from  the  original 
meanings  of  words.  The  unit  is  more«valuable  than  its  deriva- 
tion. 

The  diopter  as  applied  to  cylinders  is  of  the  same  signifi- 
cance as  when  applied  to  spherical  lenses,  but  it  applies  to  the 
meridian  of  highest  power  at  right  angles  to  the  axis  of  the 
cylinder.  Cylinders  are  neutral  in  one  meridian  only — the  axial 
meridian.  In  all  oblique  meridians  their  power  is  proportional 
to  their  nearness  to  the  meridian  of  highest  power. 

VALUE  OF  NOTATION. 

With  this  notation  for  waves  of  light  and  the  notation  of 
optical  instruments  now  in  general  use,  it  is  possible  to  describe 
optical  phenomena  or  effects  with  precision.  It  makes  the 
foundation  of  optometry  complete,  and  the  two  notations  are 
always  numerically  equal,  because  based  upon  the  meter.  We 
should  note  here  that  this  system  of  notation  of  curvature  is 
quite  as  applicable  to  the  curvature  of  lenses  and  mirrors  as  to 


(DO  GENERAL    OPTICAL    PRINCIPLES. 

waves  of  light,  and  provides  a  simple  means  of  determining 
the  curvature  of  lenses  or  mirrors  of  a  given  dioptric  power, 
of  which  later.  Another  important  point  is  this:  the  notation 
is  applicable  to  the  waves  of  a  pencil  considered  individually, 
not  to  pencils  considered  collectively.  Diffusion,  for  instance, 
is  an  effect  that  pertains  to  individual  pencils,  while  magnifi- 
cation is  an  effect  that  pertains  to  a  group  of  pencils.  Only  one 
pencil  of  light  is  necessary  to  produce  diffusion;  an  indefinite 
number  of  pencils  are  required  to  produce  magnification.  An 
example  of  the  consequences  of  confusing  the  two  ideas  is 
found  in  a  popular  work  on  skiascopy,  in  which,  in  the  author's 
analysis  of  the  effects  at  the  retina  of  the  observed  eye,  or  area 
3,  these  two  distinct  phenomena  are  hopelessly  entangled,  and 
we  find  the  author  speaking  gravely  of  the  "magnification" 
resulting  from  the  action  of  the  dioptric  media  of  the  eye  upon 
a  single  pencil  of  light,  and  of  the  indefinite  "magnification"  of 
a  point  in  the  retina.  At  least  two  points  and  two  pencils  are 
necessary  for  magnification,  for  if  there  are  not  two  points 
how  can  they  be  separated,  since  magnification  is  separation  of 
points,  or  an  enlargement  of  the  retinal  image.  But  we  will  dis- 
cuss this  matter  more  fully  in  its  appropriate  place.  Chapter  IV. 

POWER  AND  CURVATURE. 

The  power  of  lenses  and  mirrors  is  proportional  to  their 
curvature.  Power  and  curvature  have,  in  each  case,  a  direct 
relation  to  each  other.  What  is  the  relation?  Power,  as  we 
have  seen,  is  the  capacity  of  a  lens  or  mirror  to  modify  the 
curvature  of  the  waves  of  light,  so  that  the  relation  of  the 
power  of  an  instrument  to  the  curvature  of  its  surface  is  the 
relation  of  its  capacity  to  modify  wave  curvature  to  the  curva- 
ture of  the  glass.  Both  curvatures  thus  pertain  to  the  glass: 
one  being  the  curvature  of  the  glass,  the  other  the  capacity  of 
the  instrument  to  modify  wave  curvature.  For  instance,  a 
+  8  D.  lens  modifies  wave  curvature  8  Cm.  in  a  positive  direc- 
tion: now  the  curvature  of  the  glass  has  a  direct  relation  or 
ratio  to  8  Cm,  What  the  relation  or  ratio  is  depends  upon  the 
index  of  refraction  of  the  glass.  The  index  of  refraction  is  not 
the  ratio,  but  it  contains  the  ratio,  as  we  shall  see. 


GENERAL    OPTICAL    PRINCIPLES.  6l 

As  a  lens  (or  mirror)  is  made  of  solid  material  its  curva- 
ture is  fixed  in  the  making,  but  the  waves  of  light  upon  which 
it  acts,- or  may  act,  are  various  and  variable  in  curvature, 
depending  primarily  upon  the  distance  of  the  object.  If  we 
can  find  the  ratio  of  the  curvature  in  the  glass  to  the  capacity 
of  the  instrument  to  modify  wave  curvature,  all  that  will  be 
required  will  be  a  simple  multiplication  or  division  to  deter- 
mine either  when  the  other  is  known.  The  ratio  is  the  multi- 
plier or  divisor,  as  the  case  may  be,  and  it  reduces  wave  curva- 
ture to  glass  curvature,  or  glass  curvature  to  wave  curvature, 
the  same  as  the  factor  i6  reduces  avoirdupois  pounds  to  ounces 
or  ounces  back  to  pounds.  But  as  the  index  of  refraction 
varies  for  different  media,  this  ratio  also  varies.  So  that  it 
would  be  a  better  comparison  to  say  that  this  ratio  is  like  price 
— the  price  of  coal.  If  coal  is  $4.50  a  ton,  4.5  is  the  index  of 
values  between  the  dollar  and  the  ton  of  coal.  Divide  the 
dollars  by  the  index,  and  you  get  the  number  of  tons  of  coal 
it  will  buy.  Multiply  the  tons  of  coal  by  4.5,  and  you  get  its 
value  in  dollars.  If  the  price  of  coal  changes,  the  problem  is  a 
new  one,  although  worked  on  the  same  plan  under  the  new 
index. 

It  the  index  of  refraction  of  the  body  of  glass  of  which  a 
lens  is  composed  is  1.60,  what  does  tfiis  mean?  It  means  pri- 
marily that  the  resistance  of  the  glass  to  the  propagation  of 
light  waves  is  1.6  times  the  resistance  of  air,  the  standard 
medium.  Light  waves  are  transmitted  in  such  glass  with 
diminished  speed.  Speed  of  the  light  waves  is  reduced  60/160 
and  remains  in  the  glass  100/160  of  its  speed  in  the  air. 
100/160  is  therefore  the  index  of  speed  in  glass,  compared  with 
speed  in  air,  the  standard  medium.  Since  1.6  =  160/100  is  the 
resistance  of  the  glass  compared  with  air,  and  100/160  is  the 
speed  of  the  waves  in  the  glass  compared  with  air,  and  these 
two  terms  are  the  inverse  of  each  other,  we  may  presume  that 
there  is  a  foundational  law  that  resistance  and  speed  are  in- 
versely proportional  to  one  another  in  a  case  of  this  kind.  The 
propagation  of  light  waves  is  not  subject  to  the  laws  of  mate- 
rial bodies  moving  through  other  material  substances — that  is, 
to  the  modifying  effects  of  friction — as  shown  by  the  fact  that 
resistance  lasts  only  while  the  wave  is  in  the  resisting  medium, 


62  GENERAL    OPTICAL    PRINCIPLES. 

and  by  the  restoration  of  the  original  speed  when  the  wave 
emerg-es  into  air.  The  delaying  influence  within  the  medium 
is  not  resistance  in  the  mechanical  sense,  but  want  of  sympathy 
with  or  responsiveness  to  molecular  motion.  It  is  a  want  of 
conductivity. 

To  generalize  the  law  we  may  represent  the  coefficient  of 
wave  velocity  in  air  by  a,  the  coefficient  of  wave  speed  in  the 
other  medium  by  b,  and  their  difference  by  c.  Then  if  a  >  h, 
which  it  usually  is,  a  =  b  -\r  c,h  =  a  —  c,  c  =  fl  —  b.  But  b/a 
=  the  ratio  of  wave  speed  in  the  other  substance  (.r)  to  wave 
speed  in  air,  for  the  ratio  of  one  quantity  to  another  is  the  quo- 
tient obtained  by  dividing  the  quantity  considered  to  be  a  part 
of  another  by  the  quantity  of  which  it  is  considered  to  be  a 
part.  Now,  if  we  take  air  as  the  standard  medium  of  resistance, 
its  resistance  is  i,  and  the  resistance  of  the  other  substance, 
whose  wave  speed  is  b/a  of  wave  speed  in  air,  is  i  ^  b/a  = 
a/b.  That  is,  the  relative  resistance  of  the  two  media,  with  the" 
resistance  of  air  as  the  standard,  is  a/b,  or  the  resistance  of  the 
other  medium  is  a/b  of  the  resistance  of  air.  Representing  the 
other  medium  by  x,  we  may  express  the  law  in  the  following 
proportions:  (i)  Wave  speed  in  x  :  wave  speed  in  air  ::  b  :  a  = 
b/a;  (2)  Resistance  in  x  :  resistance  in  air  : :  a  :  6  =  a/&;  from 
which  it  appears  that  a/b,  the  ratio  of  resistance  in  x  to  resist- 
ance in  air,  is  the  inverse  of  the  ratio  of  wave  speed  in  x  to 
wave  speed  in  air,  and  the  so-called  index  of  refraction,  or 
index  of  resistance  of  x,  with  air  as  the  standard.  But  c,  the 
difference  between  the  coefficient  of  speed,  is  c/a  of  a  and  c/b 
of  b,  and  c/a  =  the  ratio  of  loss  of  wave  speed  in  x  to  wave 
speed  in  air;  and  c/b  =  the  ratio  of  loss  of  wave  speed  in  x  to 
actual  speed  in  x.  But,  since  a/b  =  the  ratio  of  resistance  in 
X  to  the  resistance  of  air,  and  a  =  b  -\-  c,  -^  =  i  +  c/b  =  the 
ratio  of  resistance  in  x  to  resistance  in  air.  If  from  the  last 
quantity,  i,  the  resistance  of  air,  be  subtracted,  the  remainder, 
c/b  is  the  ratio  of  loss  of  speed  in  x  to  actual  speed  in  x. 

When  light  waves  pass  from  air  into  a  medium  of  greater 
resistance  they  lose  c  speed,  or  c/a  of  preceding  speed,  a.  But 
when  they  pass  from  such  medium  of  greater  resistance  into  air 
again,  they  gain  c  speed,  or  c/b  of  preceding  speed,  b,  which 
restores  them  to  a  speed  again,  for  c/a  of  o  =  c,  and  c/b  of  b 


GENERAL    OPTICAL    PRINCIPLES. 


63 


=  c,  and  therefore  c/a  oi  a  =  c/b  of  b.  If  the  resisting  sub- 
stance is  glass  with  an  index  of  refraction  of  1.60,  we  may  let 
160  represent  wave  speed  in  air;  100  will  then  represent  wave 
speed  in  the  glass,  and  60  will  represent  loss  of  wave  speed  in 
passing  from  air  into  the  glass.  Wave  speed  in  glass  is  then 
100/160  of  wave  speed  in  air;  loss  of  wave  speed  is  60/160  of 
wave  speed  in  air.  But  the  resistance  of  the  glass  is  160/100 
of  the  resistance  of  air.  At  the  incident  surface,  the  waves  lose 
60/160  of  their  previous  speed,  160;  but  at  the  emergent  sur- 
face they  gain  60/100  of  their  preceding  speed  of  100,  which 
restores  them  to  their  original  speed  in  air,  160.  The  gain  in 
speed  at  the  surface  of  emergence  exactly  compensates  for  their 
loss  of  speed  at  the  surface  of  incidence.  We  may  now  deter- 
mine the  effects  upon  the  curvature  of  the  waves  of  such 
resistance,  and  show  the  relation  of  resistance  to  refraction. 


Fig.  19 


..W_5 


vAA^v\ 


-B^'^'Vv/V.. 


A  spherical  wave  of  light  cannot  fall  upon  the  surface  of 
a  medium  of  different  resistance  at  all  points  simultaneously 
unless  the  surface  of  the  resisting  substance  conforms  exactly 
with  the  wave,  a  necessarily  rare  occurrence.  The  point  in 
the  wave  first  to  reach  the  surface  of  resistance  is  the  one  pur- 
suing a  course  perpendicular  to  such  surface.  In  Fig.  19  let 
M  represent  a  point  in  air,  A  B  the  plane  surface  of  a  resisting 
medium  whose  index  of  refraction  is  1.5,  and  let  M  P  be  per- 
pendicular to  A  B,  and  i^  be  a  point  in  ^  5  i^  times  M  P  from 
M.  Now,  a  wave  of  light  from  M  would  expand  in  all  direc- 
tions from  M,  and  along  the  radial  lines  M  P  and  M  K,  at  the 
same  rate  of  speed.  We  may  consider  the  spaces  between  the 
circular  lines  as  wave  intervals,  and  M  P  as  embracing  two 


64  GENERAL    OPTICAL    PRINCIPLES. 

such  intervals,  while  il/  K  embraces  three.  The  resistance  of 
the  glass  would  be  applied  to  the  wave  first  at  P  and  then  suc- 
cessively at  all  points  from  P  to  K.  When  the  wave  reaches 
P  on  M  P  it  will  reach  E  on  M  K,  and  while  the  wave  is  ad- 
vancing one  interval,  or  from  £  to  i^  on  il/  K,  it  will  also 
advance  along  P  D  though  but  f  of  the  distance  to  D  be- 
cause of  the  resistance  of  the  glass.  All  points  in  the  wave 
between  P  and  E,  will,  during  the  next  interval  of  time,  travel 
partly  in  air  and  partly  in  glass,  the  relative  distances  each 
travels  depending  upon  its  nearness  to  E  at  the  beginning  of 
the  interval  of  time,  or  to  K  at  the  end  of  it.  But  each  wave 
point  is  retarded  during  the  interval  relative  to  its  nearness  to 
P  at  the  beginning,  or  0  at  the  end  of  the  interval.  The  result 
of  resistance  applied  in  this  way  is  the  reformation  of  the  wave, 
or  its  change  of  curvature  for  an  amount  in  excess  of  that 
which  would  be  produced  by  natural  evolution  either  in  air  or 
glass.  If  E,  and  all  points  on  arc  E  P,  traveled  in  glass," 
natural  evolution  would  reduce  the  curvature  in  the  inverse 
ratio  of  M  P  to  M  0,  and  the  wave  would  extend  from  0  to 
F;  but  if  P,  and  all  points  on  P  E,  traveled  in  air,  natural  evo- 
lution would  reduce  the  curvature  in  inverse  ratio  of  M  P  to 
M  Dot  M  EtoM  K.  But,  M  P  :  M  0  : :  2  :  2|  =  |;  and  M  P: 
M  D  : :  2  :  3  =  f .  But  the  wave  really  extends  from  0  to  K, 
and  to  determine  the  curvature  at  either  0  or  K,  the  modifying 
effect  of  the  resistance  of  the  glass  must  be  determined.  The 
curvature  of  the  wave  at  either  0  or  K  may  be  considered  as 
consisting  of  three  elements:  (i)  The  natural  curvature  evolved 
from  M  to  P  or  from  M  to  i^  in  the  air,  (2)  the  modifying 
effect  of  the  resistance  of  the  glass  at  P  or  K,  and  (3)  the  evo- 
lution of  curvature  within  the  glass  from  0  or  K  onward.  At 
K  the  third  factor  is  zero,  but  just  within  the  glass  the  other 
factors  have  operated.  But  at  0  the  three  factors  have 
operated.  Assuming  that  the  wave  form  0  to  i^  is  spherical 
its  curvature  at  i^  is  as  L  T  to  iv  P,  the  sines  of  equal  circles, 
one  for  angle  n,  the  other  for  angle  m.  But  L  T  :  P  K 
L  K  :  H  K,  whatever  the  former  ratio  may  be.  But  L  T 
P  K  ::  P  0  :  P  D  =  f ,  as  heretofore  shown.  Hence  L  K 
H  K  ::  2  :  3,  or  //  /v  is  i^  times  L  K  or  its  equal  il/  K,  and  tlie 
curvature  of  the  wave  at  K  anterior  to  the  glass,  is  to  its  curva- 


GENERAL    OPTICAL    PRIN'CIPLES.  65 

tiire  of  the  wave  at  K  posterior  to  the  glass  as  2  is  to  3,  or  f . 
The  reduction  of  curvature  at  K,  considered  as  a  small  area 
of  A  B,  is  therefore  -J.  It  may  be  proved  that  the  reduction 
of  curvature  at  any  point  on  F  X'  is  also  -J,  and  hence  at  P  the 
reduction  is  ^-.  But  a  reduction  of  ^  at  F  places  the  center  of 
curvature  of  the  wave  at  P  within  the  glass  at  i^  P  M  from  P 
or  at  G,  which  is  nearer  M  than  H.  At  all  points  between 
P  and  K  the  new  center  of  curvature  will  be  between  G  and  H. 
The  curvature  at  0  in  the  glass  is  greater  than  the  curvature 
at  K  in  the  glass,  because  the  evolution  of  curvature,  or  reduc- 
tion of  curvature,  between  P  and  0  in  the  glass,  has  been  less 
than  reduction  of  curvature  between  E  and  K  in  air,  both  of 
which  are  evolutionary  elements.  Hence,  although  modifica- 
tion produced  by  the  resistance  of  the  glass  at  all  points  is  the 
same  (|  reduction  of  previous  curvature)  0  is  forward  of  the 
spherical  arc  having  H  K  a.s  a  radius  and  centering  at  H.  For 
a  considerable  angle  such  as  in  the  variation  of  curvature  is 
considerable,  but  for  small  pencils  of  light  it  is  slight  and  the 
curvature  at  K  and  0  may  be  regarded  as  practically  the  same. 
This  difiference  of  centers  for  the  single  wave  is  spherical  aber- 
ration, of  which  we  will  have  more  to  say  later. 

The  primary  optical  effect  in  the  above  is  the  reduction 
in  the  speed  of  the  wave  c/a  or  ^,  due  'to  the  increasing  resist- 
ance of  the  glass,  and  the  application  of  such  resistance  to 
different  points  of  the  wave  successively.  As  a  result  of  such 
reduction  of  speed  so  applied,  curvature  is  reduced  the  same 
amount,  c/a  =  -J,  and  becomes,  at  the  point  of  incidence 
b/d  —  f  of  previous  curvature,  at  which  the  evolutionary  fac- 
tor becomes  the  same  again  for  all  areas.  But  at  the  second 
surface  or  surface  of  emergence,  the  wave  is  accelerated  c/b  = 
^  of  previous  speed,  and  at  a  plane  surface  the  wave  emerges 
at  D  first  and  K'  last.  Curvature  is  modified  at  the  second 
surface  in  the  same  ratio,  c/b,  that  speed  is  modified.  As  a 
result  curvature  at  K'  and  D  becomes  c/b  =  ^  greater,  and  the 
new  center  of  curvature  for  K'  is  at  a  point  on  H  D  ^  oi  H  K' 
from  K'.  This,  as  it  is  a  restoration  of  wave  speed,  is  also  a 
restoration  of  curvature,  or  would  be  but  for  the  evolutionary 
element  acting  during  the  interval  in  which  the  wave  is  pass- 
ing through  the  glass.     The  two   effects   at  the  two  plane 


66  GENERAL    OPTICAL    PRINCIPLES. 

surfaces  neutralize  each  other  for  c/a  of  a  —  c/b  of  b,  but  the 
•evolutionary  element  is  not  of  course  neutralized.  Every 
index  of  refraction,  so-called,  is  the  index  of  resistance  of  the 
two  media,  air  being  the  standard  or  divisor,  for  the  index  of 
resistance  being  a/b,  and  a  =  b  -{-  c,  -^^  =  i  +  c/b.  In 
the  index  1.6,  .6  =  c/b.  In  an  index  1.52,  .52  =  c/b.  The 
index  of  resistance  is  always  i  +  c/b  which  is  always  equal  to 
a/b. 

Now,  this  ratio,  c/b,  is  also  the  ratio  of  the  curvature  of 
the  glass  on  both  surfaces  of  a  lens  to  its  capacity  to  modify 
the  curvature  of  waves  of  light.  If  one  surface  of  the  lens  has 
a  curvature  of  +  20  Cm.  (convex  with  2  in.  radius)  and  the 
other  surface  has  a  curvature  of  +  8  Cm.  (convex  the  other 
way,  with  5  in.  radius)  both  surfaces  have  a  combined  positive 
curvature  of  +  28  Cm.  If  the  index  of  refraction  is  1.52,  c/b 
=  .52.  Now  this  lens  will  modify  the  curvature  of  a  wave  ot 
light  .52  of  28  Cm.  =  14.56  Cm.,  and  as  both  modifications  are 
in  the  positive  direction,  it  is  a  +  14.56  D.  lens.  The  given 
lens  is  what  is  known  as  a  bi-convex  lens,  although  the  curva- 
ture of  its  two  faces  are  opposite ;  but  as  one  is  a  surface  of  in- 
cidence and  the  other  is  a  surface  of  emergence,  both  are  posi- 
tive to  positive  waves  of  light.  Its  entire  curvature  is  +  28  Cm, 
w^hether  its  two  faces  are  as  given,  or  each  has  a  curvature  cf 
+  14  Cm.,  or  if  one  surface  is  plane  and  the  other  has  a  curva- 
ture of  +  28  Cm.  If  the  lens  were  periscopic,  one  surface  hav- 
ing a  curvature  of  —  5  Cm.,  the  other  would  need  to  have  a 
curvature  of  +  33  Cm.,  so  that  there  would  be  +  5  Cm.  to  neu- 
tralize the  —  5  Cm.  and  +  28  Cm.  to  spare.  But  in  the  above 
lenses,  each  of  +  28  Cm-,  and  of  +  14.56  D.  power,  the  focal 
point  of  a  pencil  of  light  would  be  slightly  different  on  account 
of  the  different  location  of  the  surfaces  \vitli  the  edge  of  the  lens 
in  one  fixed  position.  The  power  of  each  lens  is,  however,  the 
same.  To  make  a  lens  of  a  specific  dioptric  power,  as  of  + 10  D., 
the  index  of  refraction  being  1.52,  the  combined  curvature  of 
its  two  surfaces  must  be  10  Cm./.52  =  19-23  Cm.  But  the  rule 
of  curvatures  does  not  apply  to  single  surfaces,  for  a  single  sur- 
face may  be  plane  and  have  power,  or  curved  and  have  no 
power,  for  its  power  depends  as  much  upon  the  curvature  of 
the  wave  as  upon  the  curvature  of  the  glass.     In  the  dioptric 


GENERAL    OPTICAL    PRIN'CIPLES.  6/ 

power  of  spherical  mirrors  the  factor  used  in  reducing  curva- 
ture to  power  or  power  to  curvature  is  2,  and  its  dioptric 
power  is  twice  its  curvature.  A  mirror  whose  radius  of  curva- 
ture is  10  in.  has  a  curvature  of  40/10  =  4  Cm.  and  a  power  of 
8  D.  If  the  mirror  is  concave  it  is  positive;  if  convex  it  is 
negative,  for  the  determined  power. 

The  use  of  factor  .52  or  c/b,  whatever  the  index  of  resist- 
ance or  refraction,  is  due  to  the  modification  of  wave  curva- 
ture produced  by  lenses.  The  indices  of  refraction  and  diverg- 
ence are  based  upon  the  index  of  resistance  of  the  two  media, 
W'ith  air  as  the  standard  or  divisor  or  second  term  of  the  ratio. 
They  are  an  effect  due  to  a  more  primary  cause — the  differ- 
ence of  resistance  of  the  two  media — the  resistance  of  the  so- 
called  refracting  substance  as  compared  with  the  resistance  of 
air.  The  index  of  refraction,  1.52,  is  primarily  the  index  of 
resistance,  the  a/h  as  hereinbefore  described;  the  index  of 
■deviation,  .52,  is  primarily  the  sum  of  effects  at  the  two  sur- 
faces of  the  refracting  body,  the  c/h  as  above  described.  If 
we  represent  the  speed  of  the  waves  in  air  by  152  =  a,  in  the 
glass  their  speed  will  be  100  =  &,  a  reduction  of  c/a  of  a,  or 
52/152  of  152  =  52,  leaving  100.  The  modification  of  wave 
curvature  is  then  c/a  or  52/152  of  previous  curvature  found 
at  the  surface  of  incidence,  whether  of  the  glass  alone,  the 
wave  alone,  or  both.  But  at  the  surface  of  emergence  speed 
is  accelerated  c/h  =  52/100  of  previous  speed,  h,  or  100; 
52/100  of  100  =  52,  and  restores  speed  to  o  again.  The  modifi- 
cation of  wave  curvature  at  the  second  surface  is  then  c/b  or 
52/100  of  all  preceding  curvature,  whether  of  the  wave  alone, 
the  glass  alone,  or  both.  Now,  if  the  convex  surface  of  a 
plano-convex  lens  intercepts  a  neutral  or  plane  wave  of  light, 
the  wave  will  be  given  a  curvature  of  c/a  =  52/152  of  the 
curvature  of  the  glass,  because  the  curvature  of  the  glass  em- 
braces all  curvature  found  at  the  surface  of  incidence.  But  at 
the  second  surface,  which  is  plane,  the  total  curvature  will  be 
in  the  wave,  and  is  52/152  of  preceding  glass  curvature  plus 
a  negligible  increase  of  curvature  evolved  in  the  glass,  greatest 
at  and  near  the  axis  of  the  lens  and  least  near  the  periphery. 
At  this  surface  curvature  is  increased  52/100  of  preceding 
curvature,  or  52/100  of  52/152  of  the  curvature  of  the  glass  at 


68  GENERAL    OPTICAL    PRINCIPLES. 

the  incident  surface.  The  total  modifying  effect  at  both  sur- 
faces, neglecting  the  evolutionary  element  produced  in  the 
glass,  is  then  52/152  +  52/100  of  52/152  of  the  curvature 
of  the  anterior  face  of  the  lens,  or  c/a  +  c/h  of  c/a.  But 
c/b  of  c/a  =  c^/ah,  and  the  entire  modification   is  c/a  + 

nil  Cb         1  o    /      J  Cb   +  C-  C  (b   +  C)     Ca  /;  rr^l         ,      • 

^•Vo&  =  ^  +  c-/ah  -  --^^^  =  -^-j^  -  ^^  =  c/b.  That  is, 
the  entire  modification  is  c/b  of  the  curvature  of  the  anterior 
face  of  the  lens.  If  the  lens  has  an  anterior  curvature  of  +  12 
Cm.  modification  of  a  plane  wave  of  light  by  it  is  .52  (c/b)  of 
12  Cm.  =  6.24  Cm.  The  lens  is  therefore  a  +  6.24  D.  lens. 
Hence  the  use  of  the  factor  .52  or  c/b  in  reducing  the  curva- 
ture of  lens  to  power.  All  lenses  are  modified  forms  of  the 
plano-convex  lens,  and  the  rule  is  applicable  to  all.  Distinc- 
tion must  be  made  for  positive  and  negative  faces,  however, 
one  of  which  tends  to  neutralize  the  other,  and  the  total  curva- 
ture is  the  excess  of  one  over  the  other. 

If  the  anterior  surface  has  a  curvature  of  +  5  Cm.  and  the 
object  is  10  in.  distant,  the  incident  waves  have  a  curvature 
of  -f  4  Cm.  The  sum  of  the  tw-o  curvatures  is  9  Cm.,  and  the 
wave  will  be  modified  at  such  anterior  surface  c/a  of  9  Cm.,  for 
it  would  be  modified  by  a  plane  surface  c/a  of  4  Cm.,  and  a 
plane  wave  would  be  modified  c/a  of  5  Cm.  by  this  surface. 
The  sum  of  the  two  effects  is  then  c/a  of  9  Cm.  =  3.0789  Cm. 
But  this  modification  does  not  complete  the  total  lens  action, 
for  a  posterior  plane  surface  must  still  be  passed,  -f  4  Cm.  — 
3.0789  Cm.  =  .9211  Cm.,  the  positive  cur\'ature  of  the  wave 
transmitted  through  the  glass.  The  posterior  plane  surface 
will  act  negatively  upon  such  positive  wave,  increasing  its 
curvature  c/b  of  .9211  Cm.,  making  it  i  H-  c/b  of  .9211  Cm.  = 
a/b  of  .9211  Cm.  =  1.5  of  .9211  Cm.  =  1.4  Cm.  The  total 
modification  is  -f  4  Cm.  —  1.4  Cm.  =  2.6  Cm.,  and  the  lens  is 
a  +  2.6  D.  lens.  Its  power  is  c/b  or  .52  of  5  Cm.,  the  curva- 
ture of  the  glass  =  2.6  Cm.  The  center  of  curvature  of  the 
wave  is  40/1.4  =  28.57  in.  anterior  to  the  glass.  By  the 
method  of  surfaces,  the  thickness  of  the  lens  being  taken  into 
account,  the  exact  position  of  the  focus,  for  the  most  central 
part  of  the  lens,  with  reference  to  either  surface  may  be  deter- 
mined. The  above  lens  will  not.  however,  focus  the  above 
pencil,  but  the  position  of  the  anterior  center  of  curvature, 


GENERAL    OPTICAL    PRINCIPLES.  69 

often  called  a  negative  focus,  though  with  little  propriety, 
may  be  exactly  ascertained. 

In  refraction  of  a  central  pencil  wave  curvature  is  modified 
but  no  deviation  is  produced,  except  in  minute  axial  pencils 
oblique  to  the  principal  axis,  and  there  are  two  deviations  of 
these,  the  one  counteracting  the  other.  But  for  peripheral 
minor  pencils  there  is  modification  of  wave  curvature  and 
deviation  also.  Modification  of  wave  curvature,  the  index  of 
refraction  being  fixed,  is  always  the  same  for  the  total  curva- 
ture of  glass  and  wave,  but  deviation  is  proportional  to  the 
distance  of  periphery  from  the  axial  area.  If  the  wave  is 
plane  only  the  curvature  of  the  glass  has  to  be  considered,  for 
a  plane  wave  is  static  the  same  as  the  glass,  with  respect  to 
curvature.  If  the  wave  is  convex  or  concave  its  curvature  is 
not  static,  and  it  will  have,  unless  it  conforms  in  curvature 
with  the  glass,  different  curvature  at  peripheral  than  at  central 
areas.  Hence  the  glass  surface  will  have  a  different  wave 
curvature  to  modify  at  different  points,  or  the  sum  of  the  two 
curvatures  (of  glass  and  wave)  will  not  be  exactly  the  same  at 
all  points.  Modification  of  curvature  is,  however,  always  the 
same,  c/a  at  the  first  surface  +  c/h  of  c/a  at  a  second  plane 
surface,  of  the  curvature  of  the  anterior  surface,  and  c/h  of  the 
curvature  of  the  posterior  surface,  making  c/h  of  the  curvature 
of  both.  Peripheral  areas  of  the  wave  are  deviated  toward  the 
axis  of  the  lens,  so  that  barring  aberration,  each  wave  finds  its 
center  at  the  same  point  upon  its  axis,  or  the  axis  of  the  lens 
that  passes  through  the  point  of  origin  of  the  pencil. 

The  factor  2  used  in  reducing  the  curvature  of  mirrors  to^ 
dioptric  power  is  due  to  the  complete  reaction  of  the  mirror. 
Its  reaction  is  not  partial  nor  fractional,  as  in  refraction,  but 
full  and  complete.  If  a  luminous  point  is  located  at  the  center 
of  curvature  of  a  concave  mirror,  the  wave  would  be  reflected 
directly  back  to  the  point  of  starting.  This  would  exactly  re- 
verse the  curvature  of  the  wave,  as  from  +  5  Cm.  to 5  Cm. 

If  the  radius  of  curvature  were  different,  the  result  would  be 
the  same.  Transposing  a  +  5  Cm.  wave  as  above  to  a  —  5  Cm. 
is  performing  10  D.  of  work,  and  the  mirror  does  exactly  the 
same  work  that  a  +  10  D,  lens  would  do.  Hence  it  is  a  +  10 
D.  mirror.     It  would  focus  neutral  waves  at  4  in.    There  are. 


70  GENERAL    OPTICAL    PRINCIPLES. 

of  course,  the  same  limitations  upon  a  mirror  as  upon  lenses, 
for  only  a  small  area  of  the  mirror  near  the  axis  can  be  used 
on  account  of  spherical  aberration,  which  causes  peripheral 
areas  to  produce  different  results. 


CHAPTER  III. 


GENERAL    OPTICAL    PRINCIPLES.       REFRACTION     OF    THE    EYE. 
COEFFICIENT    OF    EMMETROPIA.      THE    DIOPTRIC    SUR- 
FACES.     TRANSITION   OF   IMAGE   IN   SKIASCOPY. 


npHE  first  work  of  the  oculist  or  optician  in  an  optical  diag- 
nosis  is  to  determine  the  capacity  of  the  dioptric  media 
with  reference  to  the  work  required  of  them — the  focusing  of 
pencils  of  light  from  the  distant  object  upon  the  retina  with 
the  employment  of  the  static  power  of  the  eye  only.  The  next 
step  is  determining  the  amount  of  its  incapacity  by  optometric 
methods,  whether  such  incapacity  pertains  to  one  or  both  eyes, 
or  to  one  or  all  meridians  of  the  same  eye.  Whether  the 
measurement  is  made  objectively  or  subjectively,  the  purpose 
is  the  same — to  produce  normal  refractive  power.  In  this 
connection  it  is  desirable  to  have  a  concise  formula  in  which 
to  express  the  eye's  dioptric  power  in' connection  with  the 
work  it  is  required  to  perform.  Such  a  formula  would  be 
compound,  except  for  emmetropic  eyes,  and  consist  of  two 
parts;  to  wit:  (i)  the  dioptric  power  required  to  enable  it  to 
focus  neutral  pencils  of  light — pencils  usually,  though  not 
necessarily,  from  the  distant  object — upon  the  retina,  and  (2) 
its  dioptric  incapacity  to  do  this  work  exactly,  either  through 
the  over  or  under  power  of  the  media,  or  want  of  symmetry 
in  diiTerent  meridians. 

eye's    DIOPTRIC   WORK, 

An  eye,  to  be  emmetropic,  must  be  able  to  focus  neutral 
pencils  in  all  meridians,  by  the  employment  of  its  static  power 
only,  exactly  upon  the  retina,  especially  at  its  most  sensitive 
area,  the  macula  lutea.  What  is  the  dioptric  power  required 
of  an  eye  in  doing  this  work  ?  It  is  different  for  different  eyes 
and  different  individuals,   ranging,   perhaps,  from  as  low  as 

71 


"^2  GENERAL   OPTICAL    PRINCIPLES. 

-{-  40  D.  to  +  60  D.  A  short  eye — one  whose  anterio-posterior 
diameter  is  short — requires  higher  dioptric  power  than  a  long 
eye,  other  things  being  equal.  But  the  length  of  the  eye  is 
not  the  only  determining  factor,  for  the  nearer  a  surface  of 
refraction  is  to  the  anterior  surface  of  the  eye,  the  more  effec- 
tive it  is,  for  that  gives  it  a  longer  distance  in  which  to  focus 
each  pencil.  A  myopic  eye  ma}^  have  less  real  dioptric  power 
than  a  hyperopic  eye,  but  on  account  of  its  longer  anterio- 
posterior diameter  less  power  be  required  of  it  to  focus  the 
pencils  at  the  more  distant  retina.  Different  emmetropic  eyes 
are  by  no  means  the  same,  for  the  same  reason.  An  eye  that, 
with  passive  accommodation,  focuses  neutral  pencils  upon  the 
retina,  is  emmetropic  whether  the  eye  be  long  or  short.  A 
short  emmetropic  eye  has  uecessaril}'  greater  static  power  than 
a  long  emmetropic  eye.  But,  disregarding  the  absolute  diop- 
try  of  an  eye  to  enable  it  to  focus  neutral  pencils  at  the  retina, 
we  may  adopt  a  literal  coefficient  to  represent  that  power.  The 
Greek  letter  "-"  will  serve  the  purpose.  Bytheterm"i  -D." 
let  that  power,  whether  it  be  40,  50  or  60  diopters,  required 
to  focus  neutral  pencils  at  the  retina,  with  passive  accommoda- 
tion, be  understood.  If  an  eye  possesses  a  static  power  of 
+  -  D.  then  it  is  emmetropic.  If  not,  it  is  either  myopic  or 
hyperopic.  If  one  or  more  meridians  of  an  eye — there  will, 
of  course,  be  more  if  there  is  one — is  hyperopic  or  myopic,  the 
eye  is  astigmatic  to  the  extent  of  the  difference  of  the  extreme 
or  principal  meridians.  +  -  D.  may  express  more  than  the 
eye's  static  power  or  it  may  express  less.  If  it  is  either  more  or 
less  the  eye  is  ametropic.  An  eye  possessing,  under  passive 
accommodation,  less  than  H  -  D.  may  gain  a  power  of  +  -  D. 
by  exercising  its  power  of  accommodation.  It  is  ametropic 
none  the  less,  for  its  static  power  is  not  equal  to  +  -  D.  If  an 
eye  requires  to  use  3  D.  of  accommodation  to  focus  neutral 
waves  upon  the  retina  or  see  the  distant  object  clearly,  its 
static  power  is  +  (-  —  3)  D.  With  3  D.  of  accommodation 
in  force  it  has  a  power  of  +  -  D.  It  may  possess  more  dynamic 
power  than  3D.  If  it  has  5  D.  of  dynamic  power,  only  2  D. 
of  such  power  is  available  for  focusing  pencils  of  light  from 
the  near  point  at  the  retina.  Its  static  power  is  -(-  ('^  —  3)  D. 
Add  +  5  D.  to  that  and  you  have  -f  (-  +  2)  D.  for  its  full 


GENERAL    OPTICAL    PRINCIPLES.  73 

power.     Its  dynamic  power  is  the  difference  between  its  static 
power  and  its  full  power,  or 

+   (r  +  2)  D. 

+  ("-3)D- 
5D. 

Such  an  eye  is,  without  regard  being  paid  to  latent  elements, 
3  D.  hyperopic  and  has  5  D.  of  accommodation. 

These  formulae  are  convenient  for  expressing  at  once  the 
work  required  of  the  dioptric  media  and  their  incapacity  to  per- 
form the  work.  What  "-"  is,  in  any  case,  we  do  not  really 
inquire  into,  but  -  —  a  expresses  a  dioptric  insufficiency, 
whether  -  be  40,  50  or  60,  and  -  -[-  3  or  r  +  a  expresses  over- 
power, and  shows  3  D.  or  a  D.  of  myopia.  We  always  want 
to  know  whether  the  eye  is  or  has  over- power  or  under -power, 
and  the  formula  shows  which  and  how  much.  It  can  be  made 
to  answer  all  the  dioptric  questions  required  in  correcting.  For 
instance,  if  the  static  and  dynamic  power  are  as  follows  : 


s. 

P.  : 

+  (- 

+ 

4) 

D. 

D. 

P.  : 

+  ('^ 

•  + 

12) 

D. 

^  D. 

■we  know  that  its  accommodation  is  8  D.;  that  the  eye  is  4  D. 
myopic  ;  that  its  punctum  remotum  is  10  in.,  and  its  punctum 
proximum  is  3^  in.  A  —  4  D.  lens  would  place  its  punctum 
remotum  at  infinity  and  its  punctum  proximum  at  5  in.  A 
record  in  this  form  for  each  diagnosis  would  be  valuable,  for  if 
the  person  came  back  complaining  of  the  glasses  the  former 
measurement  would  be  on  record.  It  is  not  often  that  glasses 
are  given  that  exactly  correct  the  degree  of  error  found,  but 
the  optician  would  know,  by  referring  to  the  record,  what  ex- 
act condition  he  found  in  the  previous  examination.  The 
glasses  brought  back  or  the  prescription  would  not  tell  him 
that  unless  he  prescribed  exactly  for  the  error  found.  The 
glasses  cannot  change  and  can  easily  be  measured  over  again, 
but  the  eyes  may  change  and  be  quite  different  than  before. 
By  a  new  diagnosis  and  a  comparison  with  the  record,  whether 
they  have  changed  or  not  and  how  much  is  readily  determined. 


74  GENERAL   OPTICAL    PRINCIPLES, 

These  formulae,  two  for  each  eye  if  refraction  is  unsym- 
metrical,  make  a  complete  statement  of  the  case.  Each  for- 
mula, or  set  of  formulae,  is  for  an  individual  eye.  The  two 
eyes  may  show  the  following  : 

Right  eye  :     S.  P.  +  (-  —  2)  D. 

D.  P.  +  (:r  +  3)  D.         Ace.  5  D. 

Left  eye:        S.  P.  +  (- —  2>^)  D. 

D.  P.  +  (-  +  2%)  D.     Ace.  5  D. 

But  the  eyes  may  be  astigmatic,  having  different  power  in 
different  meridians.  In  that  case  a  formula  would  be  required 
for  each  chief  meridian,  as  above.  Supposing  the  principal 
meridians  to  be  90°  and  180°,  the  formulae  may  be  as  follows 
for  right  eye: 

Right  eye  :     180°  S.  P.  (-  —  2)  D. 

D.  P.  (-  +  3)  D.     Ace.  5  D. 
90°  S.  P.  (-—  i)  D. 

D.  P.  (-  +  4)  D.      Ace.  5  D. 

Showing  two  diopters  of  hyperopia  in  180°  and  one  diopter 
in  90°,  and,  hence,  one  diopter  of  astigmatism.  The  refrac- 
tion of  the  other  eye  could  be  formulated  in  the  same  manner. 
Of  course,  these  formulae  do  not  express  the  eye's  real 
dioptric  power,  for  "-"  in  the  term  "+  -  D. "  is  an  undeter- 
mined quantity.  But  in  skiascopy  it  is  of  great  importance  to 
comprehend  this  coefficient  of  power — not  absolutely,  but  rela- 
tive to  the  three  surfaces  of  refraction — for  this  gives  a  com- 
prehension of  the  appearances  when  the  observing  eye  is  at  or 
near  the  so-called  area  of  reversal. 

REFRACTING  SURFACES. 

The  dioptric  power  of  the  eye  is  primarily  the  sum  of  the 
refractive  effects  at  three  surfaces.     These  surfaces  are: 
(i)  The  anterior  surface  of  the  cornea. 

(2)  The  anterior  surface  of  the  crystalline  lens. 

(3)  The  posterior  surface  of  the  crystalline  lens. 

It  will  be  convenient  to  refer  to  these  surfaces  by  letter^ 
and  we  will  call  them,  in  the  order  named  above,  surfaces 
r,  .f  and  t — that  is: 


GENERAL    OPTICAL   PRINCIPLES.  75 

r  —  anterior  surface  of  cornea. 

^  =  anterior  surface  of  lens. 

t  —  posterior  surface  of  lens. 

Of  these  three  refracting  surfaces  r  is  by  far  the  most 
effective  in  proportion  to  its  curvature.  Unless  the  pencils 
have  been  modified  anterior  to  r  by  a  lens  or  mirror  the  waves 
come  to  it  as  natural  convex  waves,  their  curvature  depending 
upon  the  nearness  of  the  object.  But,  if  modified  by  a  pre- 
ceding lens  or  mirror,  they  may  be  any  sort  of  waves.  If  the 
pencils  are  natural  (not  optically  modified)  r,  which  is  positive 
for  all  positive  waves,  reduces  such  curvature.  Of  the  thou- 
sands or  millions  of  series  of  natural  waves  of  light  speeding 
through  space  toward  the  eye  from  every  direction,  none  can 
conform  with  it  in  curvature  since  it  is  convex  in  the  other 
direction  and  its  curvature  is  opposite  to  the  curvature  of  all 
waves  that  can  reach  it.  But  this  surface  is  specially  effective 
because  it  has  the  benefit  of  its  full  index  of  refraction,  1.33 
because  it  receives,  and  is  the  only  surface  to  receive,  pencils 
of  light  from  air.  It  resists  the  waves  or  transmits  them  at  f 
of  their  speed  in  air  from  which  they  come,  or  takes  away  ^ 
of  their  speed,  or  reduces  wave  length  ^.  The  crystalline  lens, 
although  it  has  a  higher  index  of  refraction,  compared  with 
air  (1.43)  receives  waves  transmitted  to' it  through  the  aqueous 
humor  or  emits  them  into  the  vitreous  humor,  both  of  which 
have  an  index  of  refraction  of  about  1.33,  the  same  as  the 
cornea.  It  therefore  does  not  delay  or  retard  the  waves  as 
much  or  shorten  wave  length  to  such  a  degree  as  the  cornea. 
The  effective  index  of  refraction  of  the  crystalline  lens  is 
1. 43/1. 33  =  1.075,  which,  compared  with  the  cornea,  is  slight, 
about  4/13  as  much,  for  equal  curvatures.  The  cornea  reduces 
wave  length  |,  and  that  wave  length  (f  of  air)  is  maintained  in 
the  aqueous  humor  to  the  lens.  The  lens  then  reduces  wave 
length  about  1/13  more,  and  hence  the  two  effects  are  as  |  tor 
1/13  for  equal  curvatures,  or  as  13  to  4. 

We  will  now  endeavor  to  trace  a  pencil  or  wave  light 
through  the  dioptric  media  of  the  eye,  considering  the  effect 
at  each  surface  of  refraction.  In  doing  this  we  will  take 
official  figures  as  to  curvatures  and  distances,  as  far  as  possible, 
but   we   must   remember   that   these    figures    are   not   to   be 


76  GENERAL   OPTICAL    PRINCIPLES. 

depended  upon,  except  in  the  most  general  way;  for  no  two 
eyes,  emmetropic  or  ametropic,  can  be  exactly  alike.  They 
are  as  different  as  finger-nails,  palm  markings  or  the  length 
of  finger-joints.  It  is  our  grossness  of  perception  that  causes 
dissimilar  things  to  appear  similar,  and  while  education 
develops  the  perceptive  faculties,  life  is  too  short  to  enable  one 
to  perceive  many  of  the  most  obvious  dissimilarities,  unless 
specially  educated  to  do  so. 

For  the  eye  under  consideration  we  will  presume  the 
radius  of  curvature  of  the  cornea  to  be  .3  in. ;  the  space  from 
r  to  s,  along  the  principal  or  optic  axis  in  static  refraction  to 
be  .11  in, ;  the  radius  of  curvature  of  5  to  be,  in  static  refraction, 
.4  in.;  the  thickness  of  the  lens  to  be  .145  in.;  and  the  indices 
of  refraction  to  be  as  already  specified.  The  radius  of  curva- 
ture of  the  posterior  surface  of  the  lens  is  given  (ofiicial)  as 
6  mm.  =  .24  in.  and  the  anterio-posterior  diameter  of  the  eye 
as  .92  in.  These  will  provide  the  data  required.  We  start  then 
with  a  plane  wave  at  the  cornea.  As  its  radius  of  curvature  is 
.3  in.  its  curvature  is  40/.3  =  133  Cm.  The  index  of  refraction 
being  1.33,  the  modifying  effect  of  the  cornea  upon  a  plane 
wave  is  c/a  =  33/133  of  the  corneal  curvature  =  33/133  of 
133  Cm.  =  33  Cm.  or  the  exercise  of  33  diopters  of  power.  The 
wave  becomes,  at  r,  a  —  33  Cm.  wave.  Its  focus  is  then  40/33 
=  1.21  in.  posterior  to  r,  or  1.21  —  .92  =  .29  in.  posterior  to  the 
retina.  But  in  passing  from  r  to  s,  through  homogeneous 
media,  the  wave  would  evolve  increased  curvature.  Since  5  is, 
according  to  hypothesis,  .11  in.  posterior  to  r,  it  is  1.21  — 
.11  =  1. 10  in.  from  the  potential  focus  of  r  when  it  reaches  s, 
or  has  a  curvature  of  40/1. 10  =  —  36.36  Cm.  At  this  point 
it  meets  the  anterior  surface  of  the  lens. 

Now,  the  curvature  of  s,  by  hypothesis,  is  40/.4  (.4  in. 
being  its  radius  of  curv^ature)  =  100  Cm.  But  as  such  curva- 
ture is  convex,  while  the  curvature  of  the  wave  is  concave,  or 
—  36.36  Cm.,  these  curvatures  are  not  opposite,  but  conforma- 
tory.  The  surface  .y  will  act  positively,  because  its  cur\-ature 
is  in  excess  of  the  curvature  of  the  wave,  100  —  36.36  =  63.64 
Cm.  As  its  available  index  of  refraction  is  1.075,  ^/^  becomes 
75/1075,  for  this  is  the  decrease  of  wave  speed,  or  wave  length, 
in  the  new  medium.     The  curvature  of  the  wave  will  then  be 


GENERAL    OPTICAL    PRINCIPLES.  TJ 

increased  75/1075  of  previous  curvature;  75/1075  of  63.64 
Cm.  —  4.44  Cm.,  and  tlie  wave  would  become  at  ^  —  36.36  — 
4.44  —  —  40.8  Cm.  The  surface  has  produced  an  effect 
amounting  to  +  4.44  diopters.  The  new  focus  of  this  wave 
would  be  40/40.8  =  .98  in.  posterior  to  s.  But  in  passing  from 
.f  to  t  through  a  practically  homogeneous  medium,  the  lens, 
it  would  evolve  increased  curvature.  Since  t  is,  by  hypothesis, 
.145  in.  posterior  to  s,  it  is  .98  in.  —  .145  in.  =  .835  in.  from 
the  potential  focus  of  s,  or  the  wave  has  a  curvature  at  t  of 
40/.835  =  47.9  Cm.,  the  incident  curvature  at  t,  the  last  dioptric 
surface.  Instead  of  determining  the  effect  of  this  surface  with 
the  official  radius  of  curvature  as  6  millimeters  or  .24  in.,  we 
will  work  the  problem  in  the  opposite  direction.  That  is,  since 
/  is  .92  in  —  (.11  in.  +  .145)  =  .92  —  .255  =  .665  in.  from  the 
retina,  the  wave  that  emerges  from  t  will  require  a  curvature 
of  40/.665  —  —  60.15  Cm.  to  focus  at  the  retina.  But  its  in- 
cident curvature  of  the  wave  at  t,  as  shown  in  the  previous 
calculation,  is  —  47.9  Cm.  It  then  must  be  increased  in  curv- 
ature 60.15  Cm.  —  47.9  Cm.  =  12.25  Cm.  That  is,  the  dioptric 
effect  of  t  must  be  12.25  Cm.  or  +  12.25  diopters.  As  this  is 
an  emergent  surface,  the  waves  will  increase  in  speed,  or  wave 
length,  c/h  =  75/1000,  and  wave  curvature  will  therefore  be 
modified  75/1000  of  the  total  curvattire  at  t.  But  75/1000  of 
the  wave  curvature  is  one  element,  and  75/1000  of  the  lens 
curvature  is  the  other,  for  since  the  curvatures  are  now  oppo- 
site, both  will,  at  this  surface,  produce  positive  refraction. 
75/1000  of  47.9  Cm.  =  3.59  Cm.,  and  12.25  Cm.  —  3.59  Cm.  = 
8.66  Cm.  that  must  be  produced  by  the  curvature  of  t,  for  3.59 
Cm.  is  exactly  what  a  plane  surface  at  t  would  do.  The  posterior 
surface  of  the  lens  must  perform  an  effect  equal  to  +  8.66 
•diopters.  To  do  that  it  will  require  a  curvature  of  8.66  -^ 
75/1000  =  8.66  X  1000/75  ~  1 1546  Cm.,  or  a  radius  of  curv- 
ature of  40/115.46  =  .346  in.,  or  .1  in.  more  than  the  official 
radius  of  curvature  of  /.  The  discrepancy  is  either  in  the  work 
or  in  the  hypotheses.  But  we  have  not  used  accurate — that  is, 
exact — data,  and  perhaps  the  discrepancy  is  the  sum  of  these. 
But  the  official  data  is  not  to  be  depended  upon  in  any  event, 
except  as  a  general  average,  the  same  as  the  length  of  the 
human  forearm. 


78  GENERAL   OPTICAL    PRINCIPLES. 

But  in  all  the  above  calculations  the  static  power  of  the 
eye  was  alone  being  considered.  In  calculating  the  dynamic 
power,  more  complicated  factors  are  introduced.  Without 
going  into  full  details,  we  may  note  the  leading  effects.  For 
instance,  if  the  object  is  S  in.  distant  from  an  emmetropic  eye, 
the  incident  waves  have  a  curvature  of  40/8  =  +  5  Cm.  Now, 
r,  although  static  in  curvature,  will  produce  a  higher  dioptric 
effect  upon  +  5  Cm.  than  upon  neutral  waves,  for  a  plane 
cornea  would  modify  the  waves  c/a  =  33/133  of  5  Cm.  But 
since  the  cornea  has  a  curvature  of  +  133  Cm.,  the  sum  of  such 
plane  modifying  surface  and  the  spherical  cornea  is  5  Cm.  + 
133  Cm.  =  138  Cm.  and  33/133  of  138  Cm.  =  34.24  Cm.  or  an 
effect  of  34.24  diopters,  which  is  33/133  of  5  Cm.  =  1.24  Cm.  = 
1.24  diopters  greater  than  the  effect  of  the  same  surface  upon  a 
plane  wave. 

But  +  5  Cm.  —  34.24  Cm.  =  —  29.24  Cm.,  the  curvature 
of  the  wave  at  r  after  refraction,  while  in  static  refraction  its 
curvature  is  —  33  Cm.  The  potential  focus  of  a  —  29.24  Cm. 
wave  is  at  a  distance  of  40/29.24  =  1.3673  in.  posterior  to  r,  or 
.4473  in.  posterior  to  the  retina.  As  in  static  refraction  the 
potential  focus  of  the  wave  at  r  is  but  .29  in.  posterior  to  the 
retina,  there  is  more  dynamic  work  to  be  done  to  make  the 
wave  focus  at  the  retina.  This  work  is  performed  in  four 
different  ways  at  once,  although  by  one  muscular  action. 

(i)  The  curvature  of  ^  is  considerably  increased  by  ciliary 
action. 

(2)  Surface  s  is  advanced  toward  surface  r,  and  the  evolu- 
tionary space  from  r  to  .?  is  decreased. 

(3)  But  surface  s,  by  such  advance,  is  farther  from  surface 
t  and  from  the  retina,  and  the  evolutionary  space  from  .y  to  Hs 
increased. 

(4)  Surface  t  is  undoubtedly  increased  slightly  in  curva- 
ture. 

These  four  factors,  combined  with  the  factor  of  increased 
dioptric  power  at  r,  together  produce  the  full  result.  Waves 
emerge  from  t  as  minus  waves  of  sufficient  curvature  to  focus  at 
the  retina.  What  part  has  each  of  these  five  factors  in  dynamic 
refraction?    That  depends  largely  upon  the  part  they  perform. 


GENERAL    OPTICAL    PRINCIPLES. 


79 


in  static  refraction.  But  no  two  emmetropic  eyes  have  the  same 
satic  refraction  even.  Can  any  one  tell  how  large  a  part  each 
of  the  different  factors  in  dynamic  refraction  plays  in  focus- 
ing- the  near  object  upon  the  retina?  No  one  can  tell,  for  even 
with  the  same  static  refraction  two  eyes  will  act  dififerently. 
Even  one  solitary  human  eye  will  not,  very  likely,  use  these 
factors  proportionately  in  focusing  pencils  of  light  from  8  inch 
and  5  inch  respectively.  The  corneal  element  is  certainly  dif- 
ferent. That  makes  the  emitted  wave  and  the  work  of  s  dif- 
ferent, but  not  proportionally  different.  The  shortening  of 
space  between  r  and  ^  cannot  be  in  the  same  proportion  as  the 
lengthening  of  space  from  .y  to  t,  and  the  dioptric  value  of  aug- 
menting the  curvature  of  ^  cannot  therefore  be  proportional  to 
such  increase  of  curvature.  This  is  a  problem  that,  with  all 
the  mathematical  training  possible  to  be  obtained,  is  hopelessly 
beyond  the  reach  of  the  most  ambitious. 

Fig.  20. 


Fig.  21. 


In  Figs.  20  and  21  we  have  represented  the  eye  in  static 
and  dynamic  refraction,  designating  the  surfaces  r,  s  and  t  as 


So  GENERAL    OPTICAL    PRINCIPLES. 

above,  and  their  respective  centers  of  curvature  as  r',  s'  and  t'. 
In  Fig.  20,  which  represents  the  position  of  the  surfaces  in 
static  refraction,  r',  the  center  of  curvature  of  the  cornea,  is  for- 
ward of  the  center  of  curvature  of  the  main  portion  or  globe  of 
the  eye,  for  it  is  but  .3  of  an  inch  from  r  while  the  center  of 
curvature  of  the  eye  is  a  little  more  than  ^  of  .92  or  .46  in.  pos- 
terior to  r.  The  position  of  r'  is  stationary  since  the  curvature 
of  r  is  unchanged,  but  is  posterior  to  f,  for  t  is  but  .11  in.  + 
.145  in.  posterior  to  r,  and  is  .3  —  .255  —  .045  in.  posterior  to  t. 
The  center  of  curvature  of  s,  its  radius  of  curvature  being  10 
millimeters  or  .4  in.,  is  .4  in.  posterior  to  .f,  or  .4  +  .1  [  =  .51  in. 
posterior  to  r.  This  is  a  trifle  posterior  to  the  center  of  curva- 
ture of  the  eye  ball.  This  center  changes  considerably  in 
dynamic  refraction,  both  on  account  of  the  advance  of  .y  toward 
r,  and  because  of  the  increased  curvature  and  shortened  radius 
of  s.  The  center  of  curvature  of  t  is  anterior  to  /.  With  a 
radius  of  curvature  of  6  mm.  or  .24  in.,  it  is  of  course  .24  in. 
forward  of  t.  But  the  cornea  is  but  .255  in.  forward  of  t,  hence 
the  center  of  curvature  of  t  would  be  but  slightly  posterior  to 
r.  In  the  computation  of  above  we  determined  the  radius  cf 
curvature  of  t  to  be  .346,  which  would  place  its  center  of  curva- 
ture anterior  to  r,  but  a  more  accurate  calculation  would  prob- 
ably place  it  very  near  r  and  slightly  posterior  to  it. 

But  in  the  calculation  of  the  efifect  of  each  dioptric  surface 
we  have  the  data  for  locating  each  potential  focus.  The  po- 
tential focus  of  the  wave  after  refraction  by  r  ( —  33  Cm.)  is, 
as  shown,  40/33  =  1.21  posterior  to  r,  or  1.21  —  .92  =  .29  in. 
posterior  to  the  retina.  In  Fig.  20  we  have  designated  this 
point  as  F".  But  since  at  .y  the  wave  becomes  —  40.8  Cm.  and 
its  center  is  .98  in.  from  s,  it  is  .98  +  .11  =  1.09  in.  from  r,  and 
1.09  —  .92  =  .17  in.  posterior  to  the  retina,  or  .29  —  .17  =  .12 
in.  anterior  to  F".  We  have  designated  this  point,  in  Fig.  20,  as 
F'.  At  /,  however,  the  wave  must  focus  at  the  retina,  or  at  F 
In  the  calculation  we  have  shown  that  to  focus  at  the  retina  ii 
must  have  or  acquire  at  t  a.  curvature  of  —  60.15  Cm.,  for  ir 
is  at  that  point  but  .665  in.  from  the  retina. 

Now,  in  dynamic  refraction,  these  factors  undergo  import- 
ant changes.  As  .y  advances  forward,  s'  would,  without  modi- 
fication of  the  curvature  of  s,  advance;  but  the  increased  curva- 


GENERAL    OPTICAL    PRINCIPLES. 


8i 


ture  of  ^  advances  the  center  s'  still  farther.  If .?  did  the  whole 
of  the  additional  +  5  D.  of  work  in  the  case  given  (the  object 
being  8  in.  from  the  cornea),  and  did  it  by  increased  curvature 
alone,  it  would  require  an  increased  curvature  of  5  -^  75/io75 
~  5  '^  ^P^  ~  71.66  Cm.,  which,  added  to  its  static  curvature 
of  100  Cm.,  would  make  its  total  dynamic  curvature  +  171.66 
Cm.,  and  its  radius  of  curvature  40  -^  171.66  =  .233  in.  But 
that  is  not  the  case,  although  increased  curvature  of  s  is  un- 
doubtedly the  largest  element  in  dynamic  refraction.  Fig.  21 
illustrates  the  variation  of  dynamic  factors  in  dynamic  refrac- 
tion, rs  is  shortened;  st  is  lengthened;  the  center  of  curvature 
of  s,  s',  advances  toward  r',  the  center  of  curvature  of  r,  or 
may  pass  it;  t'  probably  recedes  a  trifle  toward  s,  and  between 
them  all  the  dynamic  work  is  done.  But  r'  remains  stationary 
although  the  cornea  does  increased  dioptric  work.  The  posi- 
tion of  the  two  potential  foci,  F"  and  F'  are  farther  posterior  to 
the  retina — at  least  F"  is — but  the  increased  power  of  s  and  its 
increased  distance  from  the  retina  will  place  F'  very  nearly  in 
the  position  it  occupies  in  static  refraction. 

Fig.  22. 


^1— Anterior  Work  +  V^i  D.    Posterior  Work  +  10  D. 
iJ— Anterior  Work -r  5  D.        Posterior  Work  +    5  D. 


Sum  +  133^  D. 
Sum  -f  10  D. 


To  understand   the   dioptric   effect  of  the   advance  of  .s 
toward  r  we  may  study  ordinary  lens  action  to  advantage.    For 


82  GENERAL   OPTICAL    PRINCIPLES. 

instance,  take  the  effects  represented  in  Fig.  22  A  and  B.  Let 
us  suppose  that  it  is  required  to  focus  a  pencil  of  Hght  from  C 
upon  a  screen  at  .B,  16  in.  away.  If  a  lens  is  placed  12  in. 
from  C  and  4  in.  from  B,  its  anterior  work  will  be  the  neutraliz- 
ing of  waves  whose  curvature  is  40/12  ==4-3^  Cm.  and  its 
posterior  work  the  focusing  of  these  neutralized  waves  at  B, 
4  inches  away.  The  lens  will  require  then  40/4  =  +  10  D. 
additional  power,  making  +  37^  D.  -}-  10  D.  =  +  13^  D.  power 
all  told.  But,  if  the  lens  is  placed  midway  between  C  and  B,  it 
will  be  required  to  do  40/8  =  +  5  D.  of  anterior  and  40/8  = 
+  5  D.  of  posterior  work,  making  but  +  10  D.  of  work  all  told. 
The  second  position,  midway  between  C  and  B,  is  the  more 
advantageous  position  of  the  two.  But  if  the  lens  is  advanced 
nearer  to  C,  as  to  within  5  in.,  +  8  D.  will  be  required  for  an- 
terior work  and  40/11  =  +  37/11  D.  for  posterior  work,  mak- 
ing +  11  7/11  D.  in  all.  Hence,  at  the  midway  point  between 
object  and  screen,  a  lens  of  a  given  dioptric  power  is  most  effec- 
tive in  focusing  a  pencil  at  the  screen.  The  advance  of  .y  in 
dynamic  refraction  is  necessarily  an  advance  toward  the  mid- 
way point,  for  the  screen  or  retina  is  less  than  one  inch  pos- 
terior to  .y  always,  and  the  object  could  not  be  seen,  except  by 
an  eye  having  an  unusual  degree  of  myopia,  at  such  distance. 
Among  the  official  data  of  the  refraction  of  the  eye  is  the  datum 
that  the  curvature  of  the  cornea  is,  in  static  refraction,  100  Cm. 
— ^that  is,  that  its  radius  of  curvature  is  10  millimeters  in  an 
emmetrope.  This  is  of  course  an  assumption  that  all  emme- 
tropic eyes  are  the  same — an  unwarranted  assumption — but  let 
that  go.  The  same  report  affirms  that  when  the  emmetrope 
is  accommodated  for  an  object  13.5  Cm.  =  13.5  -^-  40  =  5.4  in., 
distant  from  the  eye,  the  curvature  of  .y  becomes  6  mm.  = 
1000/6  =  i66|  Cm.,  or  that  its  curvature  is  increased  from  100 
Cm.  to  i66|  Cm.  At  this  distance  the  dioptric  media  have 
40/5.4  =  7.4  D.  anterior  work  to  perform,  and  according  to 
official  theories  the  extra  66|  Cm.  of  .y  does  it.  But  such  in- 
creased curvature  is  not  alone  sufficient,  for  the  effect  of  s 
would  be  but  75/1075  of  66|  Cm.  =4.65  Cm.  greater  on  account 
of  such  increased  curvature  alone,  which  lacks  7.4  —  4.65  = 
2.75  Cm.  of  being  enough  if  .y  was  unchanged  in  position  and 
unassisted  in  the  dynamic  work  by  other  dynamic  factors.    But 


GENERAL    OPTICAL    PRINCIPLES.  83 

with  such  increased  curvature,  and  the  advance  of  ^  toward  r, 
and  the  dynamic  work  performed  by  r,  and  alteration  of  the 
evolutionary  space  sf,  and  a  shght  increase  of  the  curvature  of 
t,  we  have  the  combination  of  dynamic  factors  that  produce  the 
desired  effect.  That  the  increased  curvature  of  s  is  the  great- 
est of  these  factors  is  undoubted,  for  the  tension  of  the  Hga- 
ment  chiefly  afifects  the  curvature  of  s,  and  its  relaxation  allows 
expansion  of  s  chiefly  or  its  increase  of  curvature.  But  it  also 
allows  its  advance  toward  r.  The  latter  is  not,  however,  an 
important  factor,  since  it  is  so  slight  in  comparison  with  other 
evolutionary  distances.  The  increased  effect  of  r  in  dynamic 
refraction  is,  however,  important.  Each  is  a  little  link  in  the 
chain  of  effects  by  which  the  dynamic  power  of  the  eye  is  ob- 
tained. But  within  the  eye,  under  normal  vision,  the  waves 
of  light  are  from  r  onward,  whether  in  static  or  dynamic  refrac- 
tion, concave  in  curvature,  the  reverse  of  natural  waves,  which 
are  always  convex. 

In  all  cases  of  natural  vision,  the  view  of  objects,  near  or 
far,  convex  waves  of  light  come  to  the  eye.  But  the  first  sur- 
face of  refraction  transposes  them — makes  them  concave,  and 
the  other  two  surfaces  increase  their  concave  curvature,  bring 
the  center  of  curvature  nearer  to  the  wave.  Each  of  the  diop- 
tric surfaces  acts  positively,  for  this  is  positive  refraction — re- 
fraction in  the  direction  of  natural  evolution.  The  evolution- 
ary spaces  in  the  eye — from  r  to  s,  from  .y  to  t,  and  from  t  to  the 
retina — increase  the  negative  curvature  of  the  waves,  and  each 
refracting  surface  within  the  eye  does  the  same.  But  r  also 
acts  in  the  direction  of  evolution,  for  it  reduces  the  curvature 
of  convex  waves.  It  over-acts,  for  it  makes  the  convex  waves 
concave.  It  w^ould  neutralize  -f-  33  Cm.  waves,  or  waves  from 
1. 2 1  in.,  but  s  and  t  together  would  be  unable  to  center  these 
waves  at  the  retina,  for  it  would  require  about  +  43.48  D.  to 
do  that,  if  the  lens  were  in  the  position  of  r,  and  more  on  ac- 
count of  its  nearness  to  the  retina. 

In  static  refraction  the  curvature  of  r  is  opposite  to  the 
slightly  convex  waves  of  light  from  infinity,  but  the  curvature 
of  .y  is  the  same  or  confirmatory,  although  greater  in  degree, 
which  makes  it  a  positive  surface.  Surface  t  is  always,  in  nat- 
ural vision,  opposite  in  curvature  to  the  waves  that  come  to  it; 


84  GENERAL   OPTICAL    PRINCIPLES. 

hence,  in  static  refraction,  t  produces  a  greater  dioptric  effect 
than  s,  both  because  it  is  opposite  in  curvature  to  the  waves 
and  because  it  has  greater  curvature  than  s.  In  our  calcula- 
tion above,  the  dioptric  effect  of  ^  is  but  +  4.44  D.,  while  that 
of  t,  even  with  a  radius  of  curvature  of  .346  in.,  is  12.25  ^^ 
With  a  radius  of  curvature  of  .24  in.  its  curvature  would  be 
40/.24  =  +  166.66  Cm.,  which,  added  to  the  curvature  of  the 
wave  of  47.9,  would  give  the  total  curvature  at  t  166.66  Cm. 
+  47.9  Cm.  =  214.56  Cm.,  and  the  dioptric  effect  at  t  would 
therefore  be  .075  of  214.56  Cm.  —  16.09  diopters.  In  dynamic 
refraction  all  the  surfaces  are  positive,  for  r  has  more  convex 
waves;  and  the  waves  at  s,  though  concave,  are  less  so,  and 
therefore  do  not  conform  with  s,  both  because  they  are  less 
concave  and  .s  is  more  convex;  and  at  t  the  two  curvatures  are 
opposite.  But,  if  by  the  action  of  a  preceding  lens  or  mirror, 
concave  waves  come  to  r  and  it  transmits  more  concave  waves 
to  s,  waves  so  concave  that  they  focus  and  are  transferred  in  the 
crystalline  lens,  and,  hence,  convex  waves  of  great  curvature 
reach  t  from  a  center  nearer  to  t  than  fs  center  of  curvature,  we 
shall  have  effects  such  as  are  produced  in  skiascopy,  and  very 
peculiar  effects  they  are.  Any  of  the  dioptric  surfaces  of  the 
eye  may,  under  these  conditions,  become  a  negative  surface,  or 
all  of  them  may  be  negative  at  the  same  time.  For  instance,  if 
a  wave  at  the  cornea  were  —  133  Cm.,  the  curvature  of  the 
cornea  being  +133  Cm.,  it  would  not  affect  the  curvature  of 
the  wave.  But  if  the  wave  were  —  153  Cm.,  refraction  at  the 
cornea  would  carry  the  focus  back  toward  its  center  of  curva- 
ture r'.  So  also,  if  a  wave  at  .s  is  —  100  Cm.,  the  curvature  of 
s  being  +  100  Cm.,  it  would  have  no  effect.  But  it  would 
refract  negatively  a  wave  of  —  120  Cm.,  or  carry  its  center  or 
potential  focus,  farther  back  toward  s'.  A  wave  also  that 
focused  posterior  to  .y  but  anterior  to  /  would  have  necessarily 
a  greater  curvature  at  t  than  the  curvature  of  t,  whose  center 
of  curvature  is  anterior  to  s.  In  that  case  t  would  be  a  negative 
surface  and  act  negatively  upon  such  waves.  In  the  case  of 
the  cornea  supposed,  it  would  reduce  the  curvature  of  the  — • 
153  Cm.  wave,  not  153  —  133  =  20  Cm.,  the  difference  be- 
tween the  two  curvatures,  but  33/133  of  20  Cm.  =  4.2  Cm.,  or 
produce  an  effect  of  —  4.2  diopters. 


GENERAL    OPTICAL    PRINCIPLES.  85 

It  is  with  this  class  of  pencils  of  light — pencils  whose 
waves  have  been  optically  transposed  by  the  dioptric  media  of 
the  observed  eye  and  that  come  to  the  observing  eye  as  con- 
cave waves — that  the  skiascopist  has  to  deal.  When  he  brings 
the  foci  to  his  eye  it  has  a  class  of  waves  to  refract  that  cannot 
be  focused  upon  the  retina  on  account  of  the  incapacity  of  the 
dioptric  media  to  do  so.  His  eye  is  not  engaged  visually  in  the 
sense  that  it  is  engaged  when  seeing  ordinary  objects  in  the 
world.  The  dioptric  surfaces,  when  the  area  of  reversal  is  at  the 
observer's  eye,  are  of  slight  effect,  for  all  the  dioptric  work 
has  been  done  by  the  observed  eye.  The  observer  or  skiascopist 
does  not  have  a  sharply  defined  image  at  his  retina,  but  large 
diffusion  circles  that,  although  they  give  abundance  of  light, 
produce  no  image  or  real  visual  effect.  The  real  image — that 
which  should  be  upon  the  retina  for  distinct  vision — is  far  out 
in  the  eye.  In  fact,  it  may  be  anywhere  in  front  of  the  retina, 
from  retina  to  cornea,  or  anterior  to  the  cornea.  Its  advance 
from  the  retina  forward  increases  diffusion  at  the  retina  until 
it  has  advanced  so  far  that  the  dioptric  surfaces  begin  to  act 
positively  again  and  to  re-focns  the  pencils  transmitted  by  the 
preceding  image.  It  will  be  interesting  to  trace  the  image,  in 
such  advance,  from  the  retina  to  and  beyond  the  cornea,  and 
consider  the  retinal  effects. 

The  purpose  of  analyzing  the  refractive  or  dioptric  value 
of  the  different  surfaces  of  refraction  has  been  to  give  the 
skiascopist  the  basis  for  understanding  the  effects  at  his  own 
retina,  but  which  he  projects  into  the  pupil  of  the  observed 
eye,  which  is  also  imaged  upon  his  retina  when  engaged  in 
refracting  these  peculiar  pencils  of  light,  especially  when  near 
the  point  of  reversal  in  the  skiascopic  examination,  or  the 
point  at  which  the  reflex  appears  to  change  its  direction  of 
motion.  We  say  "appears,"  because  the  image  on  the  retina 
of  the  observed  eye  does  not  change  its  direction  of  motion 
actually.  Reversal  of  motion  actually  takes  place  on  the  retina 
of  the  observer's,  the  skiascopist's,  own  eye.  and  is  projected 
as  reversal  of  motion  at  the  pupil  of  the  observed  eye. 

In  Fig.  23,  C  D  is  a  luminous  arrow  and  A  B  a.  concave 
mirror,  center  of  curvature  M,  and  CMC  and  D  M  D'  are 
lines  axial  to  the  mirror.     Bv  reflection  at  A  B  an  inverted 


86  GENERAL    OPTICAL    PRINCIPLES. 

image  would  fall  upon  a  screen  placed  so  as  to  intercept  the 
foci  at  C  D'.  Not  only  is  a  pencil  from  C  focused  at  C  and 
one  from  D  at  D',  but  a  pencil  from  each  point  of  C  I>  is 
focused  somewhere  along  C  D'.  All  the  pencils  focus  along 
C  D',  whether  the  screen  is  there  or  not.  If  it  is  not  there 
each  pencil  is  transposed  at  its  focus  and  proceeds  onward. 

Fig.  23. 


Before  reaching  C  D'  each  pencil  is  composed  of  concave 
waves  on  the  way  to  their  focus,  but  after  passing  C  D'  the 
waves  of  each  pencil  become  convex  again.  Beyond  C  D', 
not  only  are  what  were  upper  pencils  lower  ones,  but  what 
was  the  upper  part  of  each  pencil  before  reaching  C  D'  be- 
comes the  lower  part  of  that  pencil  beyond  C  D'.  The  image 
at  C  D'  is  an  inverted  image,  and  each  pencil  is,  Ave  may  say, 
inverted  at  C  D'. 

We  wish  now,  without  having  a  screen  at  C  D',  to  study 
the  effect  upon  the  retina  of  an  observing  eye  that  looks  into 
or  at  the  mirror  from  points  at,  anterior  to  and  posterior  to 
C  D' — that  is,  the  appearances  of  the  virtual  image,  apparently 
back  of  the  mirror,  but  really  nowhere  except  upon  the  retina 
of  the  observing  eye,  which  projects  it  into  space.  We  first 
consider  the  effects  when  the  eye  is  at  R,  forward  of  C  D'  or 
between  C  D'  and  the  mirror.  As  the  pencils  of  light  that 
reach  the  eye  at  R  have  been  transposed  by  the  mirror  from 
positive  to  negative  w^aves,  the  eye  will  receive  nothing  but 


GENERAL    OPTICAL    PRINCIPLES.  87 

negative  waves — waves  on  their  way  to  their  foci  or  potential 
foci  at  C  D'.  If  the  eye  at  R  is  emmetropic,  with  passive  ac- 
commodation, what  can  it  do  with  these  waves?  As  in  such 
state  it  focuses  neutral  waves  at  the  retina  it  will  evidently 
focus  these  pencils  forward  of  the  retina,  forming  a  true  image 
or  focal  area  forward  of  the  retina.  The  dynamic  power  of  the 
eye,  if  used,  will  be  of  no  assistance  to  it,  for  it  will  bring  the 
focal  area  farther  forward,  and  there  is  no  dioptric  resource  in 
the  eye  to  enable  it  to  focus  these  pencils  at  the  retina.  With 
this  focal  area  or  the  true  image  forward  of  the  retina  there 
will  be,  necessarily,  diffusion  circles  at  the  retina: 

But  will  the  eye  receive  pencils  or  waves  from  every  point 
in  CD?  Perhaps  it  will  at  R,  but  a  little  above  R  it  would  be 
out  of  range  of  the  pencil  from  C,  which  would  pass  entirely 
below  it;  and  a  little  below  R  it  would  be  out  of  range  of  the 
pencil  from  D,  which  would  pass  above  it.  The  same  would 
be  true  if  the  eye  were  moved  to  the  right  or  the  left,  although 
the  pencils  have  a  narrower  range  in  those  directions.  There 
will  be  diffusion  circles  upon  the  retina  of  the  eye  at  R  and  an 
enlarged  image  there,  but  the  image  will  not  be  a  distinct  one. 
It  is  a  product  of  diffusion  circles,  instead  of  exact  foci.  But  if 
the  eye  at  R  were  hyperopic  it  might  receive  just  the  assistance 
it  required  to  enable  it  to  focus  the  pencils.  It  would  receive 
that  assistance  at  some  point  between  the  mirror  and  C  D\ 
Its  position  for  such  assistance  would  depend  upon  the  degree 
of  hyperopia,  and  it  would  receive  more  and  more  assistance^ 
up  to  that  degree,  the  greater  its  distance  from  the  mirror.  At 
5  in.  from  C  D'  it  would  receive  8  diopters,  at  4  in.  10  D., 
at  2  in.  20  D.,  for  these  negative  waves  increase  in  curvature 
as  they  approach  their  foci.  The  most  hyperopic  eye  would 
receive  waves  it  could  not  possibly  focus  at  the  retina  consid- 
erably forward  of  C  D'. 

A  myopic  eye  would  have  more  difficulty  at  R  than  an 
emmetropic  eye,  and  diffusion  circles  would  be  larger,  because 
the  focal  area,  which  is  forward  of  the  retina  for  neutral 
pencils,  would  be  still  farther  forward  for  these  peculiar  pencils. 
It  would  be  the  same  if  A  B  were  a  plane  mirror  and  a  plus 
lens,  whose  focus  of  the  reflected  pencils  was  at  C  D',  were 
held  between  the  eye  and  the  mirror;  or  if  the  glass  of  the 


OO  GENERAL    OPTICAL    PRINCIPLES. 

mirror  were  plano-convex  and  the  amalgam  were  spread  upon 
its  plane  posterior  surface.  Diffusion  is  unavoidable,  except 
for  a  hyperopic  eye,  of  the  exact  degree  of  hyperopia  re- 
quired, at  R.  The  effect  of  diffusion  at  the  retina  must  not  be 
confounded  with  magnification,  but  the  distinction  between 
these  two  different  optical  results  will  be  explained  fully  in  the 
next  chapter. 

We  will  now  consider  the  eft'ects  of  the  recession  of  the 
eye  from  R  toward  C  D'  and  finally  to  C  D'  and  thence  to  R', 
and  will  study  these  effects  with  special  reference  to: 

(i)  The  capacity  and  action  of  the  eye's  dioptric  media, 
and  retinal  results,  and 

(2)  The  limitations  upon  the  number  of  pencils  that  may 
find  access  into  the  eye. 

At  R  an  emmetropic  eye  certainly  cannot  focus  these 
negative  pencils  at  the  retina.  The  true  image  or  focal  area 
of  these  pencils,  in  an  emmetropic  eye,  is  necessarily  forward 
of  the  retina,  and  at  the  retina  there  are  overlapping  diffusion 
circles,  producing  an  image,  but  not  a  sharp  definition,  such  as 
is  required  for  perfect  vision.  The  emmetropic  eye  is,  as  it 
were,  myopic  for  these  negative  pencils,  while  the  myopic  eye 
as,  in  the  same  sense,  more  myopic.  But  recession  of  the  eye 
toward  C  D'  only  makes  a  bad  matter  worse,  for  the  curvature 
of  the  waves  of  each  pencil  constantly  increases  toward  C  D', 
and  the  incapacity  or  over-capacity  of  the  dioptric  media  grows 
constantly  greater.  But  recession  also  carries  the  eye  or  pupil 
out  of  range  of  more  and  more  pencils  from  the  mirror,  or 
from  the  arrow  C  D  hy  way  of  the  mirror.  Even  that  which 
the  eye  sees  imperfectly  on  account  of  diffusion  is  limited  in 
one  way  by  limitations  upon  the  number  of  pencils  that  find 
the  pupil,  but  each  pencil  provides  the  eye  with  more  and 
more  of  its  light,  so  that  the  volume  or  intensity  of  light  at  the 
retina  increases  rather  than  diminishes. 

As  the  eye  continues  to  recede  toward  C  D',  the  focal  area 
or  image  within  it  forward  of  the  retina  advances,  and  diffusion 
circles  at  the  retina  grow.  Eventually  the  focal  area  reaches 
one  of  the  dioptric  surfaces,  t  (Fig.  24  A),  but  before  reaching 
/  even,  it  must  reach  and  pass  s',  the  center  of  curvature  of  s. 


GENERAL    OPTICAL    PRINCIPLES. 


89 


and  then  r',  the  center  for  r.  When  it  reaches  the  center  of 
curvature  of  s,  the  refraction  of  r  and  t  as  well  as  the  refraction 
of  ^  help  to  place  it  there;  but  when  the  wave  at  s  becomes 
—  100  Cm.,  wherever  the  image  or  real  focal  area,  s  ceases  to 
be  a  positive  surface;  and  whenever  the  incident  waves  at  r 


become  —  133  Cm.,  r  ceases  to  be  a  positive  surface;  and  when- 
ever the  waves  at  t  are  positive,  but  of  greater  curvature  than 
/,  t  becomes  a  negative  surface,  which  occurs  the  moment 
that  the  focal  area  passes  t  in  its  advance.     When  the  focal 


90  GENERAL   OPTICAL    PRIN'CIPLES. 

area  is  within  the  lens  it  is  forward  of  the  center  of  curvature 
of  r  and  ^  and  back  of  the  center  of  curvature  of  t,  and  all  three 
surfaces  are  negative.  But  when  the  focal  area  passes  ^\,  s 
becomes  a  positive  surface  again.  It  is  at  this  position  that  the 
work  of  re-focusing  the  pencils  from  the  image  begins.  The 
action  of  .s^  is  slight  on  the  very  convex  waves,  but  it  soon  re- 
duces their  curvature  to  such  an  extent  that  the  waves  at  t  are 
made  less  convex  than  t,  and  t  becomes  a  positive  surface. 
But  r  remains  negative  until  the  focal  area  passes  out  of  the 
eye  altogether.  When  the  focal  area  is  at  m  n,  Fig.  24  A,  diffu- 
sion at  the  retina  is  slight.  But  when  it  reaches  m  n,  Fig.  24  B, 
diffusion  has  become  wide.  But  diffusion  reaches  the  max- 
imum when  the  focal  area  is  at  or  just  forward  of  .y — that  is, 
about  at  the  pupil — for  then,  although  .y  has  become  positive, 
r  and  /  are  both  negative,  and  there  can  be  nothing  resembling 
an  image  at  the  retina.  But  few  pencils  find  access  to  the  eye; 
but  the  whole  intensity  of  the  pencils  that  do  find  access  is 
poured  into  the  eye,  producing  a  brilliant  illumination  of  the 
retina,  but  no  image.  It  is  no  doubt  between  .y  and  r  that 
positive  refraction  becomes  sufficient  to  produce  an  effect  in 
re-focusing  the  pencils,  and  re-focusing  means,  of  course,  re- 
inversion  of  the  image  upon  the  retina  and  reversal  of  motion. 
All  of  these  effects,  it  will  be  borne  in  mind,  are  at  the  retina 
of  the  observing,  not  the  observed,  eye.  When  the  eye  reaches 
C  D' ,  all  the  surfaces  become  positive,  but  even  with  surface  r 
to  help,  r,  .s  and  t  are  not  sufficient  to  refocus  the  pencils,  or 
produce  an  accurate  image. 

Further  recession  of  the  eye,  Fig.  23,  reduces  the  curv- 
ature at  r  of  these  very  convex  waves.  The  eye  soon  reaches 
a  position  in  which,  with  the  use  of  the  accommodation,  it  gets 
a  tolerably  accurate  image.  Such  image  is,  of  course,  an  in- 
version of  the  aerial  image  at  C  D',  or  corresponds  to  the 
original  C  D.  It  is  because  this  image  is  erect  on  the  retina  of 
the  observing  eye  that  the  object  or  arrow  appears  inverted 
and  motion  is  reversed.  Somewhere  between  R  and  R',  Fig.  23, 
motion  is  reversed,  because  the  image  is  re-inverted  on  the 
retina.  In  the  observing  eye  it  is  luidoubtedly  at  or  very  near 
the  plane  of  the  pupil.  It  may  be  at  the  cornea,  or  at  the  point 
where  all  three  surfaces  become  positive,  but  these  points  are 


GENERAL   OPTICAL    PRINCIPLES.  9I 

not  widely  separated,  and  the  image  passes  out  of  the  eye 
almost  as  soon  as  it  reaches  the  pupil. 

The  image  C  D'  in  the  above  corresponds  to  the  area  of 
reversal  in  skiascopy.  There  is,  however,  a  focal  area  within 
the  observed  eye  that  may  be  regarded  as  the  area  of  reversal 
also.  This  area  of  reversal  within  the  eye  comes  to  the  surface 
only  when  C  D'  is  at  the  cornea,  but  reversal  itself  may  occur 
before  the  eye  reaches  this  point.  Some  writers  have  placed 
the  area  of  reversal,  or  plane  of  reversal,  within  the  eye,  at  the 
nodal  point.  We  cannot  consider  this  to  be  correct,  for  the 
focal  area  is  at  the  nodal  points  when  all  three  dioptric  sur- 
faces are  acting  negatively,  and  nothing  tends  to  lessen,  but 
everything  tends  to  increase  diffusion.  The  nodal  point  is  a 
sort  of  convenient  optical  peg  on  which  to  hang  any  old 
optical  garment  that  cannot  be  satisfactorily  placed  elsewhere. 
Undoubtedly  reversal  occurs  just  as  diffusion  at  the  retina 
reaches  the  maximum.  We  are  inclined  on  that  account  to 
place  it  at  the  pupil.  But  when  it  is  at  the  pupil  the  cornea  is 
acting  negatively,  and  the  potential  foci  of  waves  at  the  cornea 
are  but  a  few  millimeters  posterior  to  it. 


CHAPTER  IV. 


GENERAL    OPTICAL    PRIN'CIPLES FOCUS,    DIFFL'SION,    ABERRA- 
TION,   INXERSION    AND    MAGNIFICATION. 


I  ^HERE  is  more  or  less  confusion  and  uncertainty  in  optical 
literature  arising  from  the  failure  to  distinguish  between 
an  optical  effect  upon  individual  pencils  of  light,  and  an  effect 
upon  a  group  or  system  of  pencils  considered  collectively.  The 
terms  focus,  diffusion  and  aberration  are  terms  that  relate  to 
individual  pencils;  inversion  pertains  to  individual  pencils  and- 
to  the  group  or  system  of  pencils  of  which  it  is  a  member;  while 
magnification  is  a  phenomenon  applying  strictly  to  an  effect 
upon  a  group  of  pencils  proceeding  from  the  same  object  and 
focused  at  the  same  area.  The  effects  upon  the  individual  pen- 
cils are  optical,  but  the  effects  upon  the  group  thus  optically 
modified  are  natural,  the  effects  of  drawing  mental  conclusions 
from  physical  appearances.     This  will  be  seen  by  analysis. 

A  FOCUS. 

The  word  "focus"  is  strictly  applicable  to  an  individual 
pencil  of  light,  really  the  center  of  curvature  of  a  series  of  con- 
cave or  negative  waves.  There  is  no  such  thing  as  the  focus 
of  a  group  of  pencils,  nor  is  the  term  properly  applicable  to  a 
lens.  If  a  system  of  positive  pencils  of  light  are  transposed  by 
the  action  of  a  lens  or  mirror  each  pencil  has  its  focus  separate 
from  the  foci  of  all  other  pencils,  and  the  assemblage  of  the  foci 
constitute  the  real  image  of  the  object.  The  lens  has  dioptric 
power  or  potency  or  capacity  to  modify  the  waves  of  light  iti 
each  pencil  or  a  group  of  pencils  transmitted  through  it.  If 
it  transposes  and  focuses  each  pencil,  such  foci  are  the  foci  of 
the  pencils,  not  of  the  lens.  By  the  reversal  of  the  curvature 
of  the  waves  their  centers  of  curvature  are  given  a  new  posi 


GENERAL    OPTICAL    PRINCIPLES.  93 

tion  in  advance  of  the  waves,  and  then,  by  natural  evolution 
(or  involution)  the  waves,  as  they  advance,  assume  a  curva- 
ture proportional  to  their  distance  from  such  center.  At  the 
■center  their  curvature  is  infinite,  and  from  that  point  convex 
waves  are  evolved. 

Waves  of  light  are  static  in  curvature  only  when  they  are 
neutral  or  plane.  This  is  due  to  their  dynamic  property  of 
-evolving  curvature  or  change  of  curvature  by  propagation 
through  space,  for  in  such  propagation  they  are  necessarily 
advancing  toward  or  receding  from  their  center  of  curvature, 
if  they  have  one.  But  plane  waves,  having  no  center  of  curva- 
ture do  not  evolve  curvature  by  propagation.  If  waves  are 
convex  they  evolve  less  and  less  curvature  until  they  become 
neutral,  or  practically  so.  If  they  are  concave  their  curvature 
increases  as  they  advance  until  they  reach  the  point  of  infinite 
curvature,  the  focus,  and  convex  waves  are  evolved.  Natural 
evolution  of  the  wave,  in  a  homogeneous  medium,  is  constantly 
in  the  direction  of  neutralization,  or  toward  the  static  state,  al- 
though, with  concave  waves,  the  point  of  infinite  curvature 
must  be  first  passed.  The  action  of  a  lens  or  mirror,  if  in  the 
-direction  of  natural  evolution,  reduces  its  work;  but,  if  in  an 
opposite  direction,  it  increases  its  work.  It  is  action  in  har- 
mony with  natural  evolution,  or  in  tlie  same  direction  as  nat- 
ural evolution,  that  makes  a  lens,  mirror  or  surface  positive; 
while  action  in  opposition  to  or  in  a  contrary  direction  from 
natural  evoluton  makes  a  lens,  mirror  or  surface  negative. 
The  optical  force  affecting  waves  of  light  is  transitory  or  im- 
pulsive, but  the  force  of  evolution  is  perpetual.  The  lens 
or  mirror  or  surface  acts  and  instantly  surrenders  the 
wave  to  the  force  of  evolution  again.  In  this  respect 
the  action  of  a  lens  or  mirror  upon  light  waves  resem- 
bles the  action  of  an  impulsive  force  upon  a  body  sub- 
ject to  the  constant  force  of  gravity.  Throw  a  body  down- 
ward and  gravity  adds  32  feet  per  second  to  its  velocity 
each  second  until  it  reaches  support.  .Throw  it  upward  and 
gravity  reduces  its  velocity  32  feet  per  second  until  it  neutral- 
izes motion  in  that  direction.  The  body  then  begins  to  fall, 
gaining  an  increment  of  32  feet  per  second  to  its  velocity  each 
second  of  its  fall.     It  passes  the  point  of  starting  with  the  same 


94  GENERAL   OPTICAL    PRINCIPLES. 

velocity  it  was  given  when  projected  upward.  Nature  trans- 
poses negative  waves  of  light  as  gravity  transposes  motion  in 
opposition  to  it.  A  positive  lens  acts  in  harmony  with  evolu- 
tion up  to  the  point  of  neutralization,  and  beyond,  for  the  lens 
has  simply  overdone  by  carrying  its  action  beyond  the  point 
of  neutralization.  Evolution  was  acting  in  the  same  direction 
before  the  lens  acted,  and  evolution  takes  up  and  follows  the 
same  direction  of  work  after  the  lens  acts.  The  action  of  a  lens 
or  mirror  is  transitory,  but  the  effect  goes  on  in  the  wave  for- 
ever. Evolution  cannot  regain  the  lost  ground  or  lost  time 
nor  eliminate  the  modification  the  optical  instrument  has  pro- 
duced. 

The  action  of  the  lens  or  mirror  is  upon  the  waves  of  the 
individual  pencils,  not  upon  the  group  or  system  of  pencils,  al- 
though the  waves  of  each  pencil  are  similarly  affected.  That 
is  a  mere  analogy.  A  focus  is  the  center  of  curvature  of  con- 
cave waves  of  light,  and  therefore  in  advance  of  the  waves  or 
in  the  direction  of  propagation  of  the  waves  which  are  neces- 
sarily proceeding  toward  it.  But  only  one  series  of  waves,  or 
one  pencil  of  light,  has  a  single  focus.  Each  other  series  of 
waves  or  pencil  has  its  center,  and  if  the  waves  are  concave, 
that  center  is  also  a  focus.  A  positive  lens  or  mirror  that  trans- 
poses the  waves  of  one  pencil  of  light  will  transpose  the  waves 
of  all  pencils  from  the  same  distance,  or  having  the  same  curva- 
ture, at  the  same  time;  but  its  action  is  none  the  less  upon  the 
waves  of  the  individual  pencils.  Where  the  focus  of  a  pencil 
may  be  depends  upon  the  efficacy  of  the  lens  for  waves  of  that 
degree  of  curvature,  as  well  as  upon  the  direction  of  propaga- 
tion of  the  waves.  The  position  of  the  focus  of  each  pencil 
depends  upon  the  same  rule.  A  focus  of  a  pencil  is  not  the 
focus  of  a  lens,  but  of  the  waves  of  light  of  which  the  pencil  is 
composed  or  of  the  pencil  of  light. 

If  an  object  is  one  meter  distant  from  a  +  5  D.  lens,  the 
lens  transposes  all  the  pencils  of  light  from  the  object.  One 
diopter  of  its  power  is  required  to  neutralize  the  +  i  Cm.  waves 
of  each  pencil  that  come  to  it,  leaving  +  4  D.  to  be  expended  in 
focusing  each  pencil.  The  foci  of  the  individual  pencils  will 
be  10  in.  from  the  lens,  but  they  will  be  at  different  points,  in 
an  area  at  right  angles  to  the  principal  axis  of  the  lens.     If  the 


GENERAL'  OPTICAL    PRINCIPLES.  95 

object  be  placed  in  the  position  of  these  foci,  lo  in.  from  the 
lens,  it  will  require  +  4  D.  of  its  power  to  neutralize  the  +  4 
Cm.  waves  that  come  to  it,  leaving  +  i  D.  with  which  to  focus 
the  pencils  at  one  meter.  The  points  on  the  opposite  sides  of 
the  lens  that  are  respectively  the  point  of  origin  and  focus  of  a 
pencil,  are  called  conjugate  foci,  for  each  is  the  potential,  if  not 
actual,  focus  of  the  other,  or  of  a  pencil  of  light  from  the  other, 
for  this  lens.  A  group  or  system  of  pencils  thus  focused,  pro- 
duces a  group  of  foci  at  about  the  same  distance  from  the  lens. 
If  a  screen  be  so  placed  as  to  react  upon  each  pencil  at  or  near 
its  focus,  it  will  display,  under  suitable  optical  conditions,  an 
inverted  image  of  the  object.  The  inversion  of  the  image  and 
its  extent  compared  with  the  object,  are  effects  of  a  different 
character  than  the  mere  transposition  of  each  pencil. 

DIFFUSION. 

This  is  also  an  eftect  upon  individual  pencils  of  light.  It 
is  the  effect  of  the  reaction  of  a  screen  at  some  other  point  or 
area,  either  posterior  or  anterior,  than  the  focus  or  focal  area. 
That  such  reaction  affects  each  pencil  of  a  group  in  the  same 
manner  and  at  the  same  time  renders  the  action  none  the  less 
an  action  upon  the  individual  pencils'.  We  can,  of  course,  see 
the  result  of  reaction  only  upon  the  group  taken  collectively, 
but  the  reaction  is  upon  the  individual  pencils.  If  the  screen 
be  held  quite  near  the  focal  area  of  the  group,  there  will  be 
developed  upon  it  a  small  diffusion  circle  for  each  pencil. 
Approach  toward  the  exact  focal  position  reduces  the  area  of 
each  diffusion  circle  and  "sharpens"  the  definition,  while  re- 
cession from  the  focal  position  enlarges  the  diffusion  circles 
and  dims  the  image.  If  the  screen  is  posterior  to  the  focal 
position  all  the  waves  reaching  it  are  convex;  but  if  it  is 
anterior  to  the  focal  position  all  the  waves  are  concave.  In 
the  former  case  the  waves  develop  upon  the  screen  from  the 
center  outward;  but  in  the  latter  case  they  develop  from  the 
circumference  of  the  diffusion  circle  inward.  The  latter  devel- 
opment also  reflects  the  waves  inward,  which  accounts  for  the 
beautiful  display  of  geometric  figures  on  the  area  of  diffusion 
when  a  bright  area  of  light  is  imaged. 


96  GENERAL   OPTICAL    PRINCIPLES. 

Fig.  25  illustrates  the  development  of  the  waves  in  a  group 
of  diffusion  circles,  each  for  an  individual  pencil  of  light.  It 
can  be  readily  seen  that,  whether  the  waves  are  developed 
from  the  center  outward  or  from  the  circumference  inward, 
they  are  proceeding,  between  centers,  in  opposite  directions. 
These  diffusion  circles  overlap,  for  each  point  on  the  screen  is 
the  center  of  a  diffusion  circle,  and  while  the  diffusion  circle 

Fig.  25. 


that  centers  at  A  is  most  intense  in  molecular  activity  at  A,  its 
activity  there  is  impaired  or  reduced  by  its  activity  at  other 
points  in  the  diffusion  circle  of  the  pencil.  But  other  pencils 
spread  their  activities  over  A  as  well  as  receive  its  activities. 
There  is,  then,  an  exchange  or  mingling  of  molecular  activities 
by  pencils  whose  diffusion  circles  overlap,  and  each  center  is 
less  individual  than  it  would  be  if  reaction  were  at  but  one 
point.  This  mingling  tends  to  destroy  the  identity  of  the  foci, 
although  the  foci  or  diffusion  circles  of  adjacent  pencils  may  be 
so  small  in  extent  as  to  preserve  a  fair  image  of  the  object.  A 
clear  definition  of  the  image  and  diffusion  circles  are  incom- 
patible on  this  account,  although  it  requires  wide  diffusion  to 
utterly  destroy  the  image.  The  loss  to  the  clearness  of  the 
image  by  diffusion  is  not  a  loss  of  light  necessarily,  but  a  loss 
of  individuality  of  the  centers  at  the  screen,  and  therefore  loss 
of  identification  of  such  centers  with  points  in  the  object. 
An  image  produced  by  diffusion  circles  lacks  distinctness 


GENERAL    OPTICAL    PRINCIPLES.  97 

in  proportion  to  the  extent  of  the  diffusion  circles.  While  the 
area  lighted  by  the  pencils  may  be  bright,  brightness  does  not 
make  the  image.  The  diffusion  circles  along  the  margin  of 
the  area  of  light  give  an  indefinite  marginal  line  to  it,  and  if, 
instead  of  circles,  the  figures  are  oblong,  on  account  of  unsym- 
metrical  refraction  (as  those  produced  by  a  sphero-cylinder), 
the  image  will  be  most  extended  in  the  direction  of  greatest 
diffusion.  But  whatever  the  effects  of  diffusion  circles  upon 
a  screen,  they  are  an  effect  upon  individual  pencils  of  light. 
The  diffuse  image  is  simply  the  sum  of  these  effects,  and 
whatever  the  dift'usion  upon  the  screen,  the  pencils  that  are 
formed  at  it  from  the  dissociated  impulses  of  the  incident  pencil 
or  pencils,  by  which  the  eye  sees  the  image,  are  composed  of 
symmetrical  or  spherical  waves  and  are  capable  of  being 
focused  by  a  lens  or  emmetropic  eye.  The  diffusion  upon 
the  screen  is  the  diffusion  of  incident  pencils  entirely.  The 
emmetropic  eye  that  views  such  image  will  obtain  a  true  pict- 
ure of  the  figure  or  effect  at  the  screen,  whether  the  incident 
pencils  be  accurately  focused  there  or  not — that  is,  of  course, 
if  the  screen  is  within  the  range  of  the  observing  eye's  accom- 
modation. In  skiascopy  there  may  be  diffusion  in  both  places, 
the  retina  of  the  observed  eye  answering  to  the  screen.  There 
is  necessarily  diffusion  at  the  retina  of  Ihe  observing  eye  when 
the  area  of  reversal  is  at  the  cornea  or  pupil,  although  if  the 
light  is  at  one  meter  and  there  is  one  diopter  of  myopia,  natural 
or  artificial,  in  the  observed  eye,  the  image  upon  the  retina  of 
the  latter  will  be  perfect  and  without  diffusion.  The  secondary 
correction  of  —  i  D.  relieves  the  observing  eye  of  its  own 
diffusion,  but  imparts  diffusion  at  the  retina  of  the  observed 
eye.  But  when  the  observed  eye,  with  passive  accommodation, 
views  the  distant  object,  or  when,  Avith  the  necessary  exercise 
of  its  accommodation,  it  views  the  near  object,  there  will  be 
no  diffusion.  Diffusion,  after  the  secondary  correction  is  made, 
is  due  to  the  nearness  of  the  luminous  area  while  the  accom- 
modation is  passive. 

SPHERICAL  ABERRATION. 

This  is  also  an  effect  upon  individual  pencils  or  the  waves 
of  individual  pencils  of  light.     We  may  obtain  a  clear  idea  of 


98 


GENERAL   OPTICAL    PRINCIPLES. 


the  nature  of  this  optical  effect  by  the  study  of  the  modifying 
influence  of  a  lens  upon  a  wave  of  light  that  is  transmitted 
throiigh  it.  It  will  serve  the  purpose  also  of  illustrating  the 
operation  of  the  rule  governing  the  relation  of  the  curvature 
of  the  glass  to  its  modifying  effect  upon  the  curvature  of  the 
waves  of  light,  stated  in  Chapter  II.     In  Fig.  26  let  A  B  he  3i 


Fig.  26. 


plano-convex  lens,  index  of  refraction,  a/b,  1.50,  theradius  of 
curvature  of  its  anterior  surface  being  2  in.,  or  its  curvature 
40/2  =  +  20  Cm.  Let  H  P  he  a  plane  or  neutral  wave  of  light 
proceeding  in  the  direction  G  C,  the  principal  axis  of  the  lens. 
At  the  point  G  the  wave  will  be  modified  in  curvature  c/a  = 
50/150  =  -^  of  the  curvature  of  the  glass.  -^  of  +  20  Cm.  = 
6J  Cm.,  and  as  the  refraction  is  positive  and  the  wave  before  re- 
fraction is  neutral,  after  refraction  its  curvature  becomes,  at  G, 
—  6J  Cm.  Its  radius  of  curvature  at  G  is  therefore  3  G  M, 
M  being  the  center  of  curvature  of  the  glass.  But  at  D  the 
wave  will  become  —  6^  Cm.  also,  and  its  radius  of  curvature 
will  be  3  D  M.  No  point  on  G  C  can  be  3  G  M  from  G  and  3 
D  M  from  D,  nor  will  the  wave  at  D  have  the  same  curvature 
as  the  wave  F,  the  point  to  which  it  has  advanced  on  G  C  while 
H  was  passing  to  D.  At  F  the  wave  will  have  a  greater  curva- 
ture than  at  D  and  its  center  is  G  F  nearer  to  G  than  the  center 
of  the  wave  at  D  is  to  D.  But  at  L  also  the  wave  will  acquire 
curvature  of  —  6^  Cm.  and  its  center  cannot  be  as  near  as  the 
center  of  V,  nor  as  distant  as  the  center  of  D.  At  F  the  wave 
will  be  G  F  nearer  its  center  than  at  G,  and  it  will  also  be  G  F 


GENERAL    OPTICAL    PRINCIPLES.  99 

nearer  its  center  than  at  D;  and  at  A'  it  will  be  G  V  nearer 
its  center  than  at  L,  and  0  will  be  L  O  =  ^'  F  nearer  its 
center  than  D.  Hence  the  wave  is  not  centered  at  one  point  or 
focus,  but  along  a  line  equal  to  G  F,  the  focus  of  F  being  near- 
est M,  and  its  focal  length  equal  to  3  G  M.  This  is  spherical 
aberration  at  the  first  surface.  But  treating  such  aberration, 
for  the  time  being,  as  a  negligible  quantity,  which  is  equivalent 
to  treating  the  thickness  of  the  glass  as  a  negligible  quantity 
also,  and  supposing  the  wave  to  be  spherical,  or  of  equal  curva- 
ture ( —  6^  Cm.)  at  D,  0  and  F,  at  the  plane  surface  of  emerg- 
ence it  will  be  again  modified  in  curvature  c/b  of  6^  Cm.  =  .50 
of  6^  Cm.  =  3^  Cm.  and  become  at  ^S  6-^  +  3^  =  —  9^1  Cm.  The 
modification  takes  place  at  ^S  before  it  does  at  T,  for  the  wave 
reaches  6"  before  it  reaches  T.  As  the  wave  is  no  longer  static 
in  curvature,  at  T  it  w'ill  have  evolved  greater  cvirvature  than 
at  6"  without  considering  its  increased  curvature  due  to  aberra- 
tion at  the  first  surface.  But  with  the  emergence  of  the  wave 
at  6^  into  air  it  will  not  only  acquire  increased  curvature,  but 
it  will  evolve  increased  curvature  from  5"  onward  i^  times  as 
rapidly.  Hence,  while  modification  at  S  and  T  will  be  equal, 
<:/b,  T  will  have  greater  incident  curvature  and  the  wave  from 
^9  onward  will  gain  curvature  or  approach  its  center  more 
rapidly  than  the  wave  from  R  until  R  also  emerges  in  air  at  T. 
When  all  points  of  the  wave  have  emerged  from  the  glass, 
evolution  of  curvature  will  be  equal  at  all  points,  but  during 
the  brief  time  that  the  wave  is  passing  from  R  to  T  peripheral 
areas  of  the  wave  will  gain  upon  central  areas,  and  tend  to 
neutralize  spherical  aberration  in  the  opposite  direction  at  the 
anterior  surface.  But  spherical  aberration  at  the  posterior 
plane  surface  will  not  neutralize  aberration  at  the  anterior  sur- 
face, since  wave  modification  is  but  c/b  =  -^  of  wave  modifica- 
tion at  the  anterior  surface.  The  new  center  of  curvature  of 
the  wave  at  S  is  c/b  oi  S  C  from  S,  or  at  P,  and  the  new  center 
of  curvature  of  the  wave  at  T  is  c/b  of  T  C'  from  T,  or  at  P'. 
Spherical  aberration  is  an  effect  produced  upon  individual 
pencils  of  light,  for  it  is  an  effect  upon  the  individual  waves  of 
a  pencil.  Other  waves  of  the  same  pencil  following  in  succes- 
sion would,  of  course,  undergo  the  same  efifects  as  those 
described  above.  The  waves  of  other  pencils  would  follow  the 
7 


lOO 


GENERAL   OPTICAL    PRINCIPLES. 


same  principle  or  rule,  or  be  governed  by  the  same  law.  But 
aberration  is  an  effect  upon  different  areas  of  one  wave  and  of 
all  the  waves  of  a  pencil,  not  a  comparison  or  relation  of  effects 
upon  different  waves.  The  law  for  each  wave  is  independent 
of  the  law  or  application  of  the  law  for  any  other  wave.  There 
is  simply  an  analogy  between  the  effects  upon  one  wave  and 
the  effects  upon  all  waves,  and  it  is  in  the  view  of  the  aberra- 
tion of  all  waves  that  w^e  observe  its  effects. 

INVERSION. 

Inversion  is  an  effect  produced  upon  the  individual  pencils 
in  that  beyond  the  focus  each  minor  pencil  is  inverted  in  posi- 
tion.   Fig.  27  represents  the  transposition  of  a  pencil  of  light 

Fig.  27  B. 


by  the  lens  A  B.  The  minor  pencils,  a  and  h,  of  the  larger 
major  pencil  are  transposed  at  C  with  the  major  pencil.  All 
focus  at  C,  but  beyond  C,  a  and  b  have  changed  positions.  All 
of  the  minor  pencils  are  inverted  in  position  in  the  same  man- 
ner; and  the  minimum  pencils,  or  rays  of  light,  are  inverted 
in  the  same  manner,  and  inversion  is  complete.  Such  inversion 
is  due  to  the  action  of  the  lens. 

But  there  is  another  inversion  than  this — the  inversion  of 
the  different  pencils  wath  reference  to  each  other.     If,  in  Fig. 


Fig.  28  A. 


# 


28,  A  B  represents  a  circular  luminous  area  3  in.  in. diameter, 
C  D  an  opaque  disc  of  the  same  size  with. a  circular  opening 


GENERAL   OPTICAL    PRINCIPLES.  lOI 

I  in,  in  diameter,  central  to  the  disc,  and  E  F  a.  circular  screen 
of  the  same  area  and  form  as  A  B,  and  the  three  be  placed  as 
represented  in  the  figure,  A  B  and  E  F  being  20  in.  apart,  and 
C  D  midway  between  them,  the  pencil  of  light  from  A  will  fall 
upon  H  F,  but  part  of  it  will  pass  below  the  disc.  The  pencil 
from  B  will,  in  like  manner,  fall  upon  G  E,  but  part  of  it  will 
pass  above  the  receiving  disc.  The  light  will  be  displayed 
upon  the  disc  as  shown  in  Fig.  28  B,  or  would  be  if  but  these 
two  pencils  illuminated  the  disc.  In  that  case  M  would  be 
illuminated  by  the  light  from  B  and  n  by  the  light  from  A. 
The  pencils  of  light  from  A  and  B  are  thus  inverted  at  the 
screen  by  natural  evolution,  and  not  by  the  action  of  a  lens. 
li  E  F  were  5  in.,  instead  of  3  in.,  in  diameter,  it  would 
intercept  all  the  light  from  A  B  hy  way  of  the  aperture  in  C  D, 
for  the  area  of  light  from  A  2I  E  F  has  twice  the  diameter  of 
the  aperture  in  C  D,  or  is  2  in.  in  diameter,  and  that  of  the 
light  from  B  is  also  2  in.,  half  of  each  falling  outside  of  the 
screen.  U  A  B  were  removed  to  the  left  to  a  position  of  20  in. 
from  C  D,  or  ii  E  F  were  removed  to  a  position  5  in.  from 
C  D,  all  the  light  from  A  B  would  be  intercepted  by  the 
screen.  But  in  their  actual  positions,  no  reduction  of  the  size 
of  the  aperture  in  C  D  would  make  either  pencil  fall  entirely 
upon  E  F,  for  to  reduce  the  two  half  pencils  that  fall  outside 
oi  E  F  ^  each,  would  close  the  aperture  in  C  D.  Enlargement 
of  the  aperture  would  increase  at  one  and  the  same  time  the 
light  upon  the  screen  and  the  amount  passing  above  and  below 
it  from  these  points. 

Fig.  29. 


But  without  changing  the  positions  oi  A  B,  C  D  or  E  F, 
or  the  size  of  the  aperture  in  C  D,  all  the  light  from  A  B 
passing  through  the  opening  may  be  made  to  fall  upon  E  F. 
This  could  be  done  by  placing  a  +  8  D.  lens  at  the  aperture, 
which  would  focus  all  the  pencils  Irom  A  B  upon  E  F,  and 
thus  prevent  the  loss  of  the  light  from  marginal  points  of  A  B. 
Fig.  29  illustrates  the  action  of  such  a  lens.    The  focus  of  the 


I02  CEXERAL   OPTICAL    PRINCIPLES. 

pencil  from  A  will  fall  at  F  or  a  trifle  above  it,  and  that  from  B 
at  E,  or  a  trifle  below  it,  on  account  of  the  slight  deviation 
toward  the  axis  of  each  pencil  within  the  lens.  The  lens  will 
produce  an  inverted  image  of  A  B  upon  E  F.  The  inversion 
of  the  image  is  not  due  to  the  inversion  of  each  pencil  at  its 
focus,  but  to  the  inversion  of  the  pencils.  The  lens  has  not 
produced  the  inversion  of  the  dififerent  pencils,  for  they  are 
inverted  without  a  lens.  They  have  inverted  themselves,  or 
are  inverted  naturally.  There  is  nothing  phenomenal  in  this 
result,  at  least  more  phenomenal  than  that  two  persons  travel- 
ing in  diagonal  directions  and  passing  through  the  same  gate- 
way should  cross  each  other's  paths.  Inversion  of  the  image 
is  nothing  more  than  a  natural  result  of  position  and  direction 
of  motion  of  moving  things.  It  is  not  due  to  the  action  of  the 
lens,  but  grows  out  of  natural  causes.  The  inversion  of  each 
pencil  is,  however,  an  optical  effect,  the  result  of  the  trans- 
position of  the  waves  of  light  in  a  pencil  of  light  by  the  action 
of  a  lens.  The  retransposition  of  the  pencil  at  the  focus  does 
not  restore  but  makes  manifest  the  inversion.  It  is  the  action 
of  the  lens  that  focuses  the  pencil;  but,  being  thus  focused, 
the  minor  pencils  are  inverted  at  the  focus  by  natural  evolu- 
tion the  same  as  different  pencils  in  the  image. 

MAGNIFICATION. 

The  direction,  size  and  distance  of  an  object  seen  is  judged 
by  the  mind.  Vision, in  connection  with  feeling, and  the  cogniz- 
ance of  space,  from  associating  time  and  muscular  energy  with 
distance,  in  a  few  brief  years  of  experience,  enable  us  to  judge 
distance,  size  and  direction  by  vision  alone.  The  retinal  images 
provide  the  data  upon  which  the  judgment  is  founded — that 
is,  the  images  upon  the  two  retinae  in  connection  with  the 
image  upon  each  retina.  An  object  at  a  distance  gives  a 
smaller  retinal  image  than  the  same  object  near  at  hand.  We 
see  a  speck  upon  the  brow  of  a  distant  ridge  to  which  the  road 
leads.  What  it  is  we  do  not  know,  but  we  may  observe  that 
its  location  relative  to  trees  and  the  general  landscape  is 
changing.  We  rightly  conclude  that  it  is  in  motion,  and  we 
know,  by  similar  comparison  with  surrounding  objects,  some- 
thing as  to  its  size.    Perhaps,  from  its  general  appearance  and 


GENERAL    OPTICAL    PRINCIPLES.  IO3 

direction  of  motion  along  the  road,  we  conclude  that  it  is  a 
conveyance  of  some  kind,  if  too  large  to  be  a  man  or  dog, 
although  we  cannot  discover  what  kind  of  a  conveyance  it  is. 
Its  nearer  approach  enlarges  the  retinal  images,  and  we  grad- 
ually make  out  a  span  of  horses  and  other  details  that  show  it 
to  be  the  stage  or  mail  coach.  The  details  become  more  and 
more  apparent  each  moment' — one  horse  is  white,  the  other  a 
bay;  the  driver  is  a  colored  man  with  a  straw  hat  on,  and  there 
is  a  boy  beside  him  on  the  driver's  seat,  and  trunk  on  the 
roof.  These  details  grow  until  the  coach  passes  along  the  road 
a  few  rods  from  where  we  stand,  and  then  begins  to  recede  in 
the  opposite  direction.  Perhaps  a  paper  has  been  thrown  out 
as  the  coach  passes,  and  a  few  minutes  later  we  are  reading 
current  history  from  printed  characters  so  minute  that  they 
cannot  be  clearly  distinguished  farther  away  than  14  in.  from 
the  eyes. 

The  difference  in  these  effects  is  due  to  the  difference  in 
the  extent  or  area  of  images  upon  the  retinae.  A  little  punctua- 
tion mark  in  the  paper  now  covers  a  larger  area  of  the  retinae 
than  the  stage  coach,  horses,  driver  and  all  a  half  hour  before. 
The  enlargement  is  due  to  the  nearness  of  the  objects.  Now, 
we  do  not  call  any  of  these  effects  magnification.  They  are 
but  natural  enlargement  of  the  image  "on  the  retinae,  due  to 
nearness.  With  a  field  glass  of  eight  diameters  magnifying 
power  the  stage  coach  at  two  miles  distance  would  appear  but 
a  quarter  of  a  mile  aw.ay,  and  the  images  upon  the  retinae 
would  occupy  eight  times  eight,  or  sixty-four  times  as  large  a 
retinal  area.  Association  and  experience  in  seeing  would  give 
the  mind,  through  the  sensatory  channels,  the  data  for  judging 
distance  and  size,  and  the  object  would  seem  one-eighth  of  its 
actual  distance  from  the  eye.  But  the  higher  intellectual  facul- 
ties would  revise  this  judgment  and  determine  the  true  cause 
of  the  analogy.  The  effects  produced  by  the  field  glass  are 
properly  termed  magnification.  Magnification  is  not  a  sensa- 
tory thing  merely,  but  it  is  a  sensatory  effect  that  natural 
sensatory  capacities  do-  not  account  for.  Magnification  is  an 
artificial  enlargement  of  retinal  images  by  optical  means  ex- 
terior to  the  eye  itself.  Such  artificial  enlargement  of  the 
retinal  image  may  produce  one  of  two  effects:    (i)  The  object 


I04  GENERAL   OPTICAL    PRINCIPLES. 

will  seem  to  be  nearer  than  it  actually  is,  or  (2)  it  will  seem  to 
be  larger  than  it  actually  is.  Sensation  accepts  the  former  in 
preference  to  the  latter  when  it  can,  for  that  is  a  matter  of  daily 
and  hourly  experience.  But  sensation  will  not  accept  nearness 
within  the  punctum  proximum  of  ordinary,  naked-eye  vision, 
for  it  has  no  experience  to  correspond  with  that.  If  a  spider's 
foot  is  within  an  inch  or  half  an  inch  of  the  eye,  which,  with 
an  assisting  positive  lens,  is  enabled  to  get  a  sharply  defined 
image  of  the  object  on  the  retina  notwithstanding  its  nearness, 
the  sensatory  verdict  is  that  it  Is  large  and  not  nearer  than  the 
ordinary  punctum  proximum.  But  the  distant  object  is  brought 
nearer  and  given  its  ordinary  size.  These  are  the  distinguish- 
ing effects  of  microscopy  and  telescopy.  Telescopy  brings  tlie 
object  nearer  and  thus  accounts  for  its  enlargement;  micro- 
scopy cannot  allow  the  object  to  be  as  near  as  it  actually  is,  but 
on  account  of  the  enlarged  image  the  object  appears,  at  the 
punctum  proximum,  proportionally  enlarged.  Both  of  these 
effects  are,  however,  magnification. 

Magnification  is  an  effect  upon  the  group  or  system  of 
pencils  of  light  from  the  object.  An  enlarged  retinal  image  is 
merely  the  separation  on  the  retina  of  the  foci  of  pencils  from 
points  in  the  object.  As  the  term  foci  pertains  to  more  than 
one  pencil,  two  or  more  pencils  are  necessarily  involved  in 
magnification.  The  foci  are  as  exactly  placed  upon  the  retina 
in  magnification  as  in  ordinary  vision,  the  only  difference  being 
in  the  separation  of  the  foci.  The  definition  is  as  sharp  in  one 
case  as  in  the  other,  or  the  principle  of  magnification  is  lost. 
If  the  pencils  do  not  focus  upon  the  retina — an  effect  pertain- 
ing to  the  individual  pencils — diffusion  results.  Diffusion 
begins  where  magnification  ends. 

It  is  in  the  confusion  of  these  two  distinct  phenomena  that 
Dr.  Jackson  is  most  unsatisfactory.  He  speaks  of  the  magnifi- 
cation of  the  retina  when  the  point  of  reversal  approaches  the 
observing  eye,  and  of  indefinite  magnification  when  it  reaches 
it.  In  skiascopy  it  is  not  the  retina  but  the  reflex  that  is  being 
observed.  The  apparent  enlargement  of  the  reflex  is  due  to 
increased  diffusion  at  the  retina,  not  of  the  observed,  but  of  the 
observing  eye,  such  diffusion  reaching  the  maximum  at  the 
moment  when  the  pencils  of  light  from  the  observed  eye  focus 


GENERAL   OPTICAL    PRINCIPLES.  I05 

at  or  just  posterior  to  the  cornea  of  the  observing  eye.  There 
may  be  diffusion  at  the  retina  of  the  observed  eye  also,  but  it  is 
slight  in  comparison  to  the  diffusion  at  area  4.  If  the  observed 
eye  is  myopic  to  the  exact  degree  required  for  it  to  focus,  with 
passive  accommodation,  the  luminous  area  upon  the  retina, 
and  no  lens  is  in  front  of  it,  it  will  focus  emergent  pencils  at 
the  same  distance  as  the  light.  If  the  observing  eye  is  at  that 
point  there  will  be  the  greatest  degree  of  diffusion  upon  its 
retina,  although  there  is  none  at  the  retina  of  the  observed 
eye.  Magnification  has  no  standing  in  these  peculiar  effects. 
The  diffusion  at  the  retina  of  the  observing  eye  is  projected  to 
the  pupil  of  the  observed  eye,  and  it  is  this  effect  that  the 
doctor  calls  indefinite  magnification.  The  doctor  also  seems 
to  think  that  a  pencil  of  light  from  one  point  on  the  retina  of 
the  observed  eye  monopolizes  the  pupillary  space  in  coming 
out.  There  is  no  chance  for  such  monopoly,  for  the  pupil 
allows  ten  million  pencils,  each  filling  its  entire  space,  to  pass 
through  it  simultaneously,  and  there  is  not  the  least  inter- 
ference between  them.  One  pencil  occupying  the  pupillary 
space  is  no  bar  to  others. 

In  emmetropia  and  hyperopia  there  is  magnification  of  the 
reflex,  for  the  reflex  is  either  at  or  within  the  focal  length  of 
the  dioptric  media.  But  neither  a  liyperope  nor  emmetrope 
will  focus  the  luminous  area  at  the  retina  without  the  use  of  the 
accommodation,  hence  there  is  diffusion  at  the  retina  of  the 
observed  eye  in  these  cases,  and  that  is  all  the  diffusion  seen 
until  a  lens  makes  the  eye  artificially  myopic.  Then  the  retina 
and  reflex  are  no  longer  nearer  than  the  focus,  and  the  emerg- 
ent pencils  are  convergent,  and  magnification  of  the  retina  or 
reflex  is  at  an  end,  the  same  as  when  a  lens  of  +  5  D.  is  held 
more  than  8  in.  from  the  object  to  be  observed  through  it,  and 
diffusion  begins. 

Fig.  30. 


Lenses  are  placed  near  the  eye,  or  at  it,  usually  to  over- 
come the  eye's  dioptric  defects,  but  they  are  placed  at  fixed 


I06  GENERAL    OPTICAL    PRINCIPLES. 

distances  from  the  object  usually  to  be  within  their  focal 
distance  from  it.  In  the  former  case  magnification  is  not  the 
thing  sought  for,  but  a  perfect  definition  at  the  retina.  In  the 
latter  case  magnification  is  the  purpose.  If  a  lens  is  at  its  focal 
distance  from  the  object,  all  its  power  being  exercised  in 
neutralizing  the  pencils,  as  shown  in  Fig.  30,  the  direction  of 
propagation  of  each  pencil  is  unchanged,  but  if  the  observing 
eye  is  far  away,  only  pencils  from  a  small  area  of  the  object 
reach  it  at  all.  But  the  im.age  of  such  small  area  will  be  en- 
larged on  the  retina  because  of  the  action  of  the  lens.  If  the 
lens  were  a  little  nearer  to  the  object  it  would  not  neutralize 
the  pencils,  and  more  pencils  from  the  object  or  from  a  larger 
area  than  A  B  would  reach  the  eye,  which  would  have  to  use 
a  little  of  its  accommodation  to  focus  them.  The  object  would 
appear  smaller,  and  magnification  would  be  less,  because  the 
retinal  image  would  be  reduced.  A  lens  used  in  this  way  gives 
its  maximum  of  magnifying  power  when  at  its  focal  distance- 
from  the  object,  or  when  it  simply  neutralizes  the  pencils.  A 
little  farther  from  the  object,  only  part  of  its  power  is  required 
to  neutralize  the  pencils,  and  it  therefore  focuses  them  posteri- 
orly at  a  greater  or  less  distance,  and  the  observing  eye, 
within  such  focal  distance,  receives  concave  waves.  An  em- 
metropic eye  has  no  capacity  to  focus  these  pencils  at  its  retina. 
A  hyperopic  eye  may  do  so  if  it  is  not  too  near  the  focus;  but 
no  eye  can  focus  them  if  at  the  focus,  for  they  are  already 
focused  by  the  lens.  Diffusion  necessarily  results,  and  diffusion 
is  at  the  maxium  when  the  observing  eye  is  at  such  focus  and 
its  dioptric  media  are  utterly  incapacitated. 

Fig.  31. 


Fig.  31  represents  an  eye,  unassisted,  focusing  pencils 
from  A  B.  The  crescent  on  the  lens  represents  the  accom- 
modation. No  accommodation  is  required  by  the  eye  in  Fig. 
30,  if  emmetropic,  as  the  waves  are  neutral.  It  will  be  noticed 
in  Fig.  30  also  that  the  lower  part  of  the  pencil  from  B  and 


GENERAL    OPTICAL    PRINCIPLES.  IO7 

the  upper  part  of  the  pencil  from  A  alone  reach  the  eye,  and 
the  source  of  the  pencil  from  A  seems  to  be  at  A'  and  that 
from  B  at  B',  because  the  foci  are  on  the  axes  A'  F  and  B'  E 
of  the  observing  eye.  In  these  two  cases  (Figs.  30  and  31)  the 
retinal  images  may  be  equal  in  extend,  although  A  B  in  Fig.  31 
is  much  larger  than  A  B  in  Fig.  30.  In  each  case  the  image  is 
inverted  at  the  retina.  Why,  then,  does  the  object  appear 
erect?  This  question  is  equivalent  to  the  question:  "Why  does 
a  feeling  feel  the  way  it  feels?"  which  is  not  ver}^  intelligible. 
Projection  of  the  two  equal  images  gives  the  idea  of  two  equal 
objects,  and  A  B  in  Fig.  30  appears  to  be  of  the  same  size  as 
A  B  in  Fig.  31.  As  they  are  at  equal  distances,  this  is  magnifi- 
cation. 


If  the  lens  in  Fig.  30  were  a  stronger  lens,  or  if  it  were 
farther  from  the  object  A  B,  it  would  transpose  all  the  pencils 
from  A  B,  giving  the  observing  ey^,  unless  it  were  beyond 
such  foci,  negative  waves.  Within  the  focal  distance  the 
obeserving  eye  would  have  negative  waves,  but  if  the  observ- 
ing eye  were  beyond  the  foci  a  true  image  oi  A  B  would  lie 
between  it  and  the  lens,  and  from  such  true  image  positive 
waves  would  be  evolved  and  pass  on  to  the  observing  eye. 
Now,  if  the  observing  eye  is  at  the  focal  area,  or  at  A'  B' ,  as 
shown  in  Fig.  32,  it  will  be  utterly  incapable  of  focusing  the 
pencils;  but  if  it  is  beyond  A'  B'  and  not  too  near,  it  may  re- 
transpose  the  pencils  transposed  at  A'  B'  and  get  an  image  of 
A  B  upon  its  retina.  But  only  minor  pencils  of  the  original 
pencils,  acted  upon  by  the  lens,  will  reach  the  observing  eye. 
The  pencil  that  focuses  at  B"  will  have  been  previously  focused 
at  B' ,  and  will  come  from  B  and  be  transposed  by  the  upper 
part  of  the  lens.  It  is  in  the  upper  position  in  the  intermediate 
image  at  A'  B',  but  in  the  lower  position  at  A"  B".  The  same 
double  inversion  will  be  noted  for  A"  from  A',  which  is  from  A. 


I08  GENERAL   OPTICAL    PRINCIPLES. 

That  is,  A"  B"  is  an  inverted  image  of  an  inverted  image,  and 
the  double  inversion  has  caused  it  to  correspond  in  position 
with  the  original  A  B.  But  the  object  will  now  appear  to  the 
observing  eye  inverted,  for  projection  produces  this  eflfect,  and 
it  is  only  when  the  retinal  image  is  inverted  that  the  object 
appears  erect. 

To  the  observing  eye  A  B  appears  enlarged  and  inverted. 
li  A  B  is,  an  arrow  pointing  upward,  the  aerial  image  A'  B' 
will  be  an  arrow  pointing  downward,  but  A"  B",  the  retinal 
image,  will  be  an  arrow  pointing  upward,  but  it  will  be  pro^ 
jected  as  an  arrow  pointing  downward,  for  that  is  the  rule  of 
projection,  a  sensatory  law  established  by  experience.  A  B 
will  be  magnified,  for  A'  B',  which  is  the  immediate  source  of 
the  pencils  that  reach  the  eye,  would  appear  larger  because  of 
nearness  to  the  observing  eye,  \l  A  B  and  A'  B'  were  equal  in 
size.  But  as  A'  B'  is  farther  from  the  lens  than  A  B  (we  will 
suppose  twice  as  far)  it  has  double  the  extent  of  A  B.  But  if 
we  also  suppose  that  A'  B'  is  double  the  distance  from  the 
dioptric  media  of  the  observing  eye  that  the  retina  is  from 
such  media,  A"  B"  will  be  of  but  ^  the  extent  of  A'  B',  and 
therefore  equal  in  extent  to  A  B.  The  retinal  image  will  be, 
therefore,  of  the  same  size  as  the  object.  Sensation  can  give 
the  data  for  but  one  conclusion  from  this — ^that  the  object  is 
large,  about  as  large  as  the  lens  that  transmits  the  pencils,  for 
it  will  not  allow  that  the  object  is  nearer  than  the  lens,  for 
the  retinal  image  of  the  lens  covers  the  image  of  A  B.  The 
lines  of  projection  for  the  lens  and  A  B  are  about  the  same. 
Since  A'  B'  is  of  twice  the  extent  oi  A  B  and  but  half  as  far 
from  the  retina,  A  B  is  magnified  four  diameters,  and  m  n 
appears  to  be  four  times  the  extent  of  A  B.  If  L  is  moved 
laterally  a  few  millimeters,  A  B  will  appear  to  move  in  the 
same  direction,  but  more  rapidly  than  the  lens. 

Magnification  is  a  sensory  eflfect  giving  data  for  a  mental 
conclusion.  The  conclusion  would  be  that  certain  objects  are 
nearer  or  larger  than  ordinary  vision  in  connection  with  the 
other  senses,  proves  them  to  be.  There  is,  fortunately,  a  higher 
court  to  decide  the  question.  That  higher  court  decides  that 
sensation  is  misleading  in  the  case;  that  its  evidence  is  to  be 
discounted,  so  far  as  it  effects  conclusions  as  to  the  nearness 


GENERAL   OPTICAL    PRINCIPLES.  IDQ 

or  size  of  the  object.  It  accepts  the  evidence  of  ordinary  vision 
and  decrees  that  the  object  is  not  nearer  nor  larger,  but  that 
superphysiological  causes  have  given  the  retina  a  larger  image 
than  it  is  naturally  entitled  to.  The  difference  between  what 
it  is  naturally  entitled  to  and  what  it  really  gets  by  reason  of 
such  superphysiological  agencies,  is  the  measure  of  the  mag- 
nification. But  the  higher  court  does  not  disdain  to  use  the 
data  of  the  misled  sensations  just  the  same.  It  accepts  them 
in  everything  except  the  trivial  matter  of  size  and  distance. 
It  acknowledges  the  existence  of  stars,  and  moons,  and  comets, 
and  nebulae  on  no  other  testimony.  It  accepts  the  proofs  of 
superphysiological  sensation,  or  rather  the  proofs  that  involve 
superphysiological  agencies,  as  if  they  were  the  results  of  the 
ordinary  and  natural  physiological  phenomena.  In  this  respect 
magnification  has  revealed  great  facts  that  could  never  have 
been  conjectured  without  it. 


CHAPTER  V. 

STATIC  FACTORS  OF  SKIASCOPY.    THE  FOUR  AREAS.    THE  THREE 

INTERVALS.       SUBSIDIARY     AREAS     AND     INTERVALS. 

ANALYSIS  OF  STATIC  FACTORS.     STATIC  EFFECTS. 


w 


■E  have  noted  in  Chapter  I  the  static  factors  of  skiascopy, 
classing  them  into  areas  and  intervals,  of  which  there 
are,  primarily,  four  areas  and  three  intervals.  It  will  now 
be  in  order  to  consider  these  factors  analytically,  and  the  part 
each  plays  in  a  simple  skiascopic  examination.  Each  factor  pos- 
sesses certain  features  it  will  be  necessary  to  take  into  account. 
The  order  in  which  we  have  named  them  is  probably  not  the' 
natural  order,  although  it  is  the  physical  order.  If  vision  were 
a  phvsical  phenomenon,  then  the  order  would  naturally  be 
phvsical.  But  as  vision  is  really  mental,  the  objective  world, 
regarded  visually,  is  a  mere  projection  of  a  mental  impression 
or  phenomenon;  and  yet  we  are  so  material  in  our  aspe:t 
toward  this  mentally  created  world  of  ours  that  we  have  no 
language  in  which  to  state  the  case  from  any  other  than  a 
material  standpoint. 

I.      THE   LUMINOUS   AREA. 

Adopting,  then,  the  physical  basis  of  treating  the  subject, 
we  begin  with  the  luminous  area.  This  we  must  regard  as  the 
basic  element,  the  preceding  cause,  the  foundation  of  all  that 
is  to  follow.  The  luminous  area  in  skiascopy  should  be  bright, 
but  not  too  bright  or  dazzling.  It  should  be  of  sufficient  ex- 
tent, neither  too  large  nor  too  small.  It  should  be  a  colorless 
light.  It  should  have  a  definite  form,  but  might  embrace  differ- 
ent forms,  as  the  circle,  the  square  and  the  triangle.  A  dark 
central  area  surrounded  by  a  ring  of  light  is  good  form. 

An  argand  burner  is  the  most  available  of  skiascopic 
lights— that  is,  of  lights  of  the  first  order.  It  can  be  procured 
almost  anywhere  in  the  country  and  is  fed  by  kerosene,  also 

110 


^   ?i 


3  o 

'"  M 

o  12 

™  > 

ft  H 

?.  o 

2; 


5'  o 

5K 


3  ' 
n 


STATIC    FACTORS    OF    SKIASCOPY. 


Ill 


procurable  in  any  place  that  would  maintain  an  optician.  Gas 
or  electric  light  are  preferable  in  the  city,  because  of  their 
-convenience  and  cleanliness,  but  they  are  little,  if  any,  better 
for  their  light  than  a  good  argand  burner.  The  Welsbach 
and  similar  lights  are  usually  regarded  as  too  brilliant,  and 
tend  to  neutralize  the  effect  of  the  dark  room  in  dilating  the 
pupil.  A  skillful  operator  will  be  very  little  handicapped  with 
any  sort  of  luminous  area,  however,  and  cases  may  be  worked 
out  accurately  by  skiascopy  with  a  tallow-candle  flame. 

To  give  form  to  the  luminous  area  and  eliminate  general 
light,  it  is  customary  to  use  a  skiascopic  chimney.  This  is  a 
hollow  cylinder  of  a'^beslos,  visually,  sufficiently  large  to  go 
•over  a  gas  or  student  lamp  chimney,  but  with  an  opening  in  it 
opposite  the  flame.  There  are  various  forms  of  these  chim- 
neys upon  the  market,  some  of  which  are  shown  in  the  figure 
•or  illustration  (Fig.  33).    The  size  of  the  opening  in  A  is  con- 


FiG.  33 A. 


trolled  by  revolving  discs,  which  bring  differently  formed 
openings  in  the  discs  before  the  opening  in  the  standard  chim- 
ney. The  extent  and  form  of  the  luminous  area  depends,  of 
course,  upon  the  extent  and  form  of  the  opening  in  these 
opaque  revolving  discs,  which  can  be  set  at  any  figure  required. 


112  STATIC    FACTORS    OF    SKIASCOPY. 

In  B  the  opening  is  practically  circular,  and  its  size  is  regulated 
by  the  little  lever  which  causes  expansion  or  contraction  of  the 
"iris  diaphragm"  over  the  opening. 

The  purposes  of  the  skiascopic  chimney  are,  then,  (i)  to 
give  the  observed  eye  a  small  area  to  focus  upon  its  retina, 
producing  a  small  image;  (2)  to  confine  the  illumination  so 
that  there  will  be  little  general  light  in  the  room;  (3)  to  control 
the  form  of  the  luminous  area,  for,  whatever  its  form,  that 
will  be  the  general  form  of  the  image  upon  the  retina  of  the 
observed  eye,  although  in  unsymmetrical  ametropia,  astig- 
matism, tlie  form  of  the  image  will  not  correspond  exactly  to 
the  luminous  area,  on  account  of  greater  diffusion  in  one 
meridian  than  that  at  right  angles  to  it.  But  symmetrical 
ametropia,  or  even  emmetropia,  with  the  area  of  light  at  a 
finite  distance  during  passive  accommodation,  gives  diffusion ; 
but  if  the  eye  is  symmetrically  ametropic — that  is,  myopic  to 
the  degree  required  to  focus  the  luminous  area  at  a  finite  dis- 
tance, even  though  accommodation  is  passive,  upon  the  retina 
— there  will  be  no  diffusion  upon  the  retina  of  the  observed 
eye,  but  such  ametropia  will  more  than  neutralize  the  emerg- 
ent pencils  and  produce  diffusion  at  the  retina  of  the  observing 
emmetropic  eye,  which  will  project  such  diffusion  into  the 
observed  eye,  causing  the  image  to  appear  to  be  diffuse  there^ 
although  it  really  is  not.  If,  with  a  plane  mirror,  the  light  from 
a  lamp  flame  is  reflected  to  a  plus  lens  in  such  position  that  it 
focuses  the  reflected  pencils  upon  a  screen,  producing  a  clear 
and  exact  definition  of  the  flame  upon  the  screen,  that  image, 
as  seen  through  the  lens  from  the  peep-hole  of  the  mirror,  would 
not  seem  to  be  clear,  for  the  lens  which  focuses  the  reflected 
pencils  from  the  flame  transposes  the  pencils  coming  from  the 
image  back  to  the  eye,  and  would  focus  them  at  the  same 
distance  as  the  flame.  The  eye  at  the  peep-hole  intercepting 
these  pencils  on  their  way  to  their  foci,  receives  concave  waves 
or  converging  rays,  which,  if  it  is  emmetropic,  it  cannot  focus 
upon  the  retina,  and  diffusion  is  unavoidable. 

Tlie  extent  of  the  luminous  area  should  be  controllable,  for 
it  may  be  necessary  to  shift  the  distance  of  the  lamp  or  light 
so  as  to  get  pencils  whose  waves  have  a  greater  curvature,  as 
in  bringing  out  the  banded  appearance  in  astigmatism ;  and  it 


STATIC    FACTORS    OF   SKIASCOPY.  II3 

should  be  possible  to  do  this  without  changing  the  extent  of 
the  retinal  image,  as  it  would  be  if  the  distance  were  changed 
without  increasing  or  decreasing  the  luminous  area.  The  use 
of  translucent  discs  has  an  effect  upon  the  interval  rather  than 
the  area  of  light,  and  will  be  considered  under  that  head. 

2.      THE   MIRROR. 

The  mirror  is  the  skiascope.  Originally  the  concave 
mirror  was  thought  to  be  the  only  serviceable  form  of  mirror 
to  be  used  for  this  purpose,  but  the  evolution  of  skiascopy  has 
brought  the  plane  mirror  more  and  more  into  favor.  The 
trained  skiascopist  will,  however,  use  both.  Aside  from  the 
confusion  that  might  result  to  beginners  by  the -opposite  action 
of  the  plane  and  concave  mirrors,  the  chief  advantage  of  using 
both  is  this,  that  with  the  plane  mirror  the  immediate  source 
of  light  is  farther  away,  necessarily,  than  the  observing  eye, 
but  with  the  concave  mirror  the  immediate  source  of  the  in- 
cident pencils  of  light  is  the  image  anterior  to  the  mirror  and 
nearer  the  observed  eye  than  the  observing  eye.  In  astig- 
matism the  banded  appearance  may  be  brought  out  with  the 
concave  mirror  by  having  the  more  distant  area  of  reversal  at 
the  observing  eye,  while  the  area  of  reversal  of  the  opposite 
meridian  is  in  front  of  it  and  near  the  immediate  source  of  light 
or  image.  The  plane  mirror  is  better  for  regular  work,  and, 
for  beginners  particularly,  it  will  prove  more  acceptable. 

The  circular  mirror  is  the  usual  form,  because  of  having 
equal  diameters  in  all  directions,  and  the  virtual  image  there- 
fore has  equal  spaces  in  which  tO'  move  when  the  mirror  is 
tilted.  The  two-inch  mirror  is  preferable  for  work  at  one 
meter,  although  that  is  a  matter  of  choice,  as  much  a  matter  of 
choice  as  the  standard  distance  at  which  to  work.  Some  cf  the 
forms  of  the  skiascope,  as  it  appears  in  the  market,  are  shown 
in  the  illustration.  The  small  mirror  with  a  dark  marginal 
area  is  a  favorite  mirror  with  many  skiascopists.  It  narrows 
the  area  of  the  major  pencils  and  produces  a  smaller  area  of 
"light  on  the  face."  This  is  a  decided  advantage  in  doing  close 
work  within  one  meter  of  the  observed  eye,  for  the  red  reflex 
will  be  seen  if  the  major  pencils  cover  the  eye,  even  at  the 
margin.     In  a  larger  mirror  the  iris  may  wholly  conceal  the 


114 


STATIC    FACTORS    OF   SKIASCOPE. 


retinal  reflex.  However,  the  question  of  size  is  a  good  deal  a 
matter  of  individual  preference.  It  is  not  unlike  the  preference 
people  have  for  different  kinds  of  steel  pens  to  do  their  writing 
with.  One  does  better  work  with  the  instrument  that  suits  him 
best. 


y¥ 


Fig.  34B. 


The  perforation  in  the  mirror  seems  also  to  be  a  matter 
of  preference,  both  as  to  size  and  kind.  In  the  market  skia- 
scopes these  vary  from  i|-  to  3  or  4  millimeters.  The  perfora- 
tion should  be  a  clean  one,  leaving  no  jagged  edges  to  reflect 
the  light  that  falls  upon  the  surfaces  and  confuse  the  observer. 
The  surface  should  be  darkened  also.  Mirrors  are  made  with 
no  perforation,  the  substitute  being  the  removal  of  a  small 
area  of  the  amalgam  from  the  back  of  the  mirror,  giving  the 
emitted  pencils  the  thickness  of  the  glass  to  pass  through  on 
their  way  to  the  observing  eye.  This  feature  is  an  improve- 
ment in  one  respect  and  a  disadvantage  in  another.  The  re- 
flection of  the  glass  answers  the  purpose  of  a  mirror  in  com- 
pleting the  retinal  image — eliminating  the  dark  area  in  it  where 
the  perforation  stands,  though  not  completely.  But  the  reflec- 
tions at  the  surfaces  of  the  glass  tend  to  obscure  the  view  of  the 
observing  eye  by  interfering  with  or  reducing  the  intensity  of 


STATIC    FACTORS    OF    SKIASCOPY  II5 

the  waves  of  emergent  pencils  when  the  area  of  reversal  or  any 
of  the  waves  of  emergent  pencils  cover  the  perforation. 

A  debatable  question  is  the  question  whether  the  observ- 
ing eye  can  see  the  red  reflex  except  when  the  virtual  image 
covers  the  perforation.  It  is  interesting  to  note  the  points  in 
the  question:  The  virtual  image,  so-called,  in  the  mirror  is  but 
a  projection  of  the  real  image  upon  the  retina  of  the  observed 
eye.  It  has  no  existence  except  to  the  eye  that  sees  it,  and  to 
that  eye  it  has  no  objective  existence.  Projection  is  a  mental, 
not  a  physical  act,  and,  speaking  physically,  the  projection  of 
the  retinal  image  and  the  image  are  one  and  the  same  thing. 
But  if  the  virtual  image  lias  no  physical  existence  it  can  have 
no  physical  location,  considered  apart  from  the  retinal  image. 
It  cannot  be  said  to  be  in  the  mirror.  The  image  of  the  flame 
or  luminous  area  is  simply  in  the  retinal  image  of  the  mirror. 
But  there  is  a  physical  mirror  as  well  as  a  retinal  image  of  the 
mirror,  neither  of  which  are  merely  mental.  There  is  also  a 
physical  luminous  area,  although,  as  we  have  seen,  the  virtual 
image  has  no  physical  existence,  except  as  an  image  at  the 
retina  of  the  observed  eye.  But  although  there  is  no  virtual 
image  anterior  to  the  observed  eye,  either  in  the  mirror  or 
elsewhere,  but  the  virtual  image  is  a  mental  creation  with  a 
real  retinal  image  for  a  foundation,  although  such  image  may 
be  imperfect  on  account  of  diffusion,  there  is  a  real  image  of 
the  retinal  image  anterior  to  an  eye  that  is,  either  naturally  or 
artificially,  myopic. 

From  the  real,  though  imperfect,  image  upon  the  retina 
of  the  observed  eye  pencils  of  light  pass,  by  way  of  the  pupil, 
out  into  space.  If  the  observed  eye  is  myopic  all  the  pencils 
focus  forward  of  the  eye,  forming  a  real  image  of  the  retinal 
image,  or  of  the  retina  with  the  image  upon  it,  true  to  life — 
clear  and  sharp  if  it  is  sharp,  or  diffuse  and  imperfect  if  it  is 
imperfect — anterior  to  the  eye.  This  is  no  mental  creation,  at 
least  not  of  the  one  whose  eye  is  under  observation,  for  he  has 
no  cognizance  of  it.  This  anterior  physical  image  must  be  in 
a  position  from  which  it  can  remit  pencils  of  light  transposed 
at  it  on  to  the  perforation  in  the  mirror  and  the  observing  eye 
back  of  it,  for  otherwise  no  reflex  will  be  seen.  Now,  the 
question  is:    Does  the  nosition  of  this  physical  image  coincide 


Il6  STATIC    FACTORS    OF   SKIASCOPE. 

with  a  mentally  created,  non-physical,  virtual  image  supposed 
to  be  in  or  back  of  the  mirror  or  some  other  impossible  place? 
The  question  brings  us  face  to  face  with  the  problem  of  visual 
projection — the  attempt  to  draw  a  line  from  a  mental  point 
to  a  point  in  the  world  corresponding  to  the  aforesaid  mental 
point  of  which  it  is  a  projection.  The  philosopher  who  desires 
to  puzzle  his  brains  over  this  question  may  do  so.  There  is  as 
much  diversion  in  it,  and  prospects  of  eventual  success,  as 
there  is  for  the  little  poodle  who  chases  his  own  tail. 

When  we  say  that  the  emergent  pencils  pursue  a  path  cor- 
responding closely  to  the  path  of  the  incident  pencils,  though 
not  coincident  with  it,  we  are  probably  coming  as  close  to 
answering  the  question  as  we  can.  That  the  emergent  pencils 
do  follow  such  a  path  is  indisputable.  But  that  they  do  not 
coincide  with  them  is  indisputable  also,  for  incident  pencils  are 
always  composed  of  convex  waves  or  diverging  rays,  while 
emergent  pencils  may  be  composed  of  convex  or  concave 
waves,  or  of  diverging  or  converging  rays.  Convex  emergent 
waves  cannot  coincide  with  convex  incident  waves,  for  they 
are  convex  in  opposite  directions.  But  neither  can  concave 
emergent  waves  coincide  with  convex  incident  waves,  unless 
their  curvature  is  the  same,  which  can  only  happen  when  the 
eye  is  accommodated  for  the  luminous  area  or  object,  which 
it  is  not  supposed  to  be  during  a  skiascopic  examination.  If 
all  the  incident  pencils  were  made  neutral  on  their  way  to  the 
observed  eye,  so  that  the  eye,  if  emmetropic,  would  focus  them 
with  passive  accommodation,  or  the  lens  that  enabled  the  diop- 
tric media  to  focus  them  upon  the  retina  would  cause  the 
emergent  pencils  to  become  neutral,  there  would  then  be  coin- 
cidence, for  the  lens  that  focused  the  incident  pencils  would 
neutralize  the  emergent  pencils.  The  emergent  pencils  reach 
the  mirror  about  the  same  area  as  that  from  which  minor  in- 
cident pencils  that  enter  the  pupil  come.  They  may  cover 
more  or  less  ground.  We  cannot  say,  however,  that  the  area 
from  which  the  incident  pencils  come  is  the  location  of  the 
virtual  image,  which  has  no  objective  location  because  it  is  not 
physical,  but  it  is  undoubtedly  the  area  to  which  we  assign  the 
mentally  projected  virtual  image;  for  if  the  mirror  is  titled,  to 
the  one  under  examination  the  virtual  image  disappears  at  the 


STATIC    FACTORS    OF   SKIASCOP7. 


117 


margin  of  the  mirror  just  as  the  last  point  in  the  area  of  "Hght 
on  the  face"  passes  off  the  pupil.  This,  however,  is  not  a  solu- 
tion of  the  problem  of  projection,  for  the  mirror,  visually  con- 
sidered, is  just  as  much  a  projection  of  a  retinal  image  as  the 
virtual  image  of  the  luminous  area  projected  to  it.  We  have 
simply  harmonized  two  projections,  or  the  projection  of  a 
smaller  area  with  the  projection  of  a  larger  area  of  which  it  is 
a  part. 

A  skiascope  has  a  handle.  To  facilitate  the  tilting  of  the 
mirror  upon  its  horizontal  axis,  it  is  customary  to  let  the 
handle  rest  between  the  third  and  fourth  fingers,  while  holding 
the  metal  butt  of  the  handle  between  the  tips  of  the  thumb  and 
forefinger.  This  enables  the  observer  to  tilt  the  mirror  in  the 
vertical,  or  upon  its  horizontal  axis,  very  slightly  and  quickly. 
The  accompanying  figure  represents  a  back  and  front  view  of  the 


Fig.  35. 

mirror  being  thus  held.  To  tilt  the  mirror  in  the  horizontal,  or 
upon  its  vertical  axis,  the  handle  should  project  downward  and 
be  grasped  lower  down.  Some  operators  prefer  to  rest  the  tips 
of  the  thumb  and  fingers  upon  the  edge  of  the  disc  in  which  the 
mirror  is  set  in  tilting  it  upon  its  horizontal  axis,  but  either 
or  any  way  of  holding  the  mirror  suitable  to  the  operator  is 
quite  proper  if  he  prefers  it.  The  mirror  is  necessarily  inclined 
at  an  angle  to  both  the  luminous  area  and  the  observed  eye  to 


Il8  STATIC    FACTORS    OF    SKIASCOPY. 

give  effect  to  the  law  of  incidence  and  reflection.  This  inclina- 
tion to  the  observed  eye  gives  a  slight  obliquity  to  the  perfora- 
tion. It  must  be  slight  or  the  observed  eye  would  be  obscured. 
All  parts  of  the  skiascope,  except  the  mirror  and  handle,  should 
be  dark  colored,  so  as  to  absorb  and  neutralize  all  light  falling 
upon  them,  especially  the  inner  surface  of  the  small  cylindrical 
perforation. 

3.       THE   OBSERVED    EYE. 

If  the  interior  of  the  eye  were  illuminated  the  observer 
would  be  able  to  see  but  a  small  area  of  the  retina,  much 
smaller  than  an  area  equal  to  the  pupillary  space,  although  it 
would  be  magnified  to  that  space.  Tliis  fact  is  due  to  the 
magnifying  effect  of  the  dioptric  media  of  the  observed  eye, 
which,  in  emmetropia,  with  passive  accommodation,  acts  as  a 
correctly  focused  positive  lens.  In  ametropia,  or  with  active 
accommodation  in  emmetropia,  the  dioptric  media  are  not, 
from  the  standpoint  of  the  observer,  focused  to  the  retina.  In 
myopia  and  emmetropia  with  active  accommodation,  the  retina 
is  back  of  the  focal  position,  while  in  hypermetropia  it  is  for- 
ward of  it.  In  the  latter  position  the  dioptric  media  have  a 
magnifying  eflfect,  the  same  as  a  positive  lens  held  nearer  the 
object  under  examination  than  the  power  of  the  lens  permits. 
Magnification  results,  but  the  lens  is  not  at  the  point  or  in  the 
position  of  maximum  magnification,  for  the  pencils  of  light  are 
not  fully  neutralized.  But  in  the  former  position  all  pencils 
from  the  retina  are  transposed,  giving  the  observing  eye,  within 
the  anterior  focal  distance,  pencils  consisting  of  concave  waves, 
or,  beyond  it,  retransposed  and  inverted  pencils  of  convex 
waves.  If  it  were  not  for  the  dioptric  media  of  the  observed 
eye,  the  observer  w'ould  see  an  area  of  the  retina  a  trifle  larger 
than  the  pupillary  space  directly  back  of  it.  The  extent  of 
such  space,  in  comparison  with  the  pupil,  would  depend  upon 
nearness.  A  dilated  pupil  would  increase  the  area  within  view 
proportionately  to  dilation.  But  the  view  of  the  retina  and 
the  image  upon  it  through  the  dioptric  media  does  not  follow 
this  simple  rule,  either  as  to  direction  or  location  or  extent, 
for  magnification  causes  a  very  small  area  of  the  retina  to  fill 
the  pupillary  space — not  a  point  to  be  sure,  but  an  area  in- 


STATIC    FACTORS    OF   SKIASCOP':^.  IIQ 

versely  proportional  to  the  distance  of  the  retina  and  observing 
eye  from  the  principal  plane  of  the  eye,  according  to  the  law 
of  images.  But  the  dioptric  media  of  the  observed  eye,  unless 
its  visual  axis  is  directed  straight  into  the  observing  eye, 
deflects  the  pencils  of  light  emerging  from  it.  The  observer 
may  thus  see  an  area  of  the  retina  and  the  image  upon  it  that 
is  actually  behind  the  iris,  and  an  area  of  the  retina  in  direct 
line  of  vision  through  the  pupil,  in  a  homogeneous  medium, 
may  be  obscured  by  the  iris.  This  is  due  to  the  deflection  of 
oblique  pencils  by  the  dioptric  media,  or  to  the  prismatic  effect 
corresponding  to  that  of  a  decentered  lens. 

In  making  skiascopic  examinations  the  observed  eye  is 
always  directed  to  a  point  in  space  to  one  side  of  the  observing 
eye,  to  avoid  stimulus  to  the  accommodation.  The  pencils 
that  reach  the  observing  eye  are  therefore  deflected.  Such 
deflection  brings  areas  of  the  retina  into  view  that  could  not 
otherwise  be  seen — areas  near  or  including  the  macula  itself. 
But  the  macula  would  be  to  one  side  of  the  area  brought  imder 
observation,  which  side  would  depend  upon  the  direction  of 
the  observed  eye  and  which  eye  (right  or  left)  were  under 
observation.  But  in  skiascopy  no  attempt  is  made  to  perceive 
the  macula  or  optic  disc,  or  to  locate  tftem  in  the  pupillary  dis- 
play. The  observer  concerns  himself  only  with  the  reflex  as  a 
whole  and  the  dark  areas  that  border  it.  He  soon  learns  the 
appearances  of  emmetropia  and  how,  with  lenses,  to  bring 
about  the  emmetropic  appearances.  Appearances  do  not  reveal 
to  him  the  conditions  that  prevail  back  of  the  dioptric  media, 
nor  is  he  anxious  to  ascertain  what  they  are  by  this  method. 
They  do  reveal  conditions  anterior  to  the  dioptric  media  which 
are  produced  by  the  dioptric  media.  If  these  conditions  are 
not  normal,  by  correcting  them  he  corrects  whatever  dioptric 
fault  there  may  be  back  of  them,  for  the  fault  is  really  neither 
posterior  nor  anterior  to  the  dioptric  media,  but  in  them. 
When  the  pupil  is  "lighted  up"  as  with  an  internal  light,  and  a 
"glow"  rather  than  a  perceptible  image  is  seen,  and  motion 
across  the  pupillary  space  is  a  mere  "flash"  having  no  apparent 
direction  of  motion,  either  with  or  against  the  mirror,  the 
anterior  image  of  the  retinal  image  in  the  observed  eye  is  at  the 
pupil  of  the  observing  eye,  and  if  the  observing  eye  is  one 


I20  STATIC   FACTORS    OF   SKIASCOPY. 

meter  in  front  of  it,  this  shows  one  diopter  of  myopia  in  the 
observed  eye. 

The  image  or  reflex,  as  seen  from  the- standpoint  of  the 
observer,  takes  on  a  bright  red  color,  due  to  a  multipHcity  of 
minute  blood-vessels  in  the  vascular  layers  of  the  posterior 
inner  surfaces.  It  is  less  red  than  blood,  because  the  capillaries 
are  spaced  by  intervening  distances  forming  a  meshwork  of 
blood-vessels.  The  retina  itself  is  transparent,  and  its  back- 
ground is  the  pigment  layer  of  the  choroid  coat.  It  is  really 
upon  this  layer,  rather  than  upon  the  retina,  the  rods  and  cones 
of  which  are  imbedded  in  it,  that  the  image  is  displayed.  A 
dark  absorbing  surface  gives  a  brighter  display  and  higher 
effect  because  of  the  contrast  it  presents  to  other  areas.  The 
areas  of  the  retina  not  displaying  the  image  of  the  luminous 
area  are  dark,  both  from  the  effect  of  the  pigment  and  the 
absence  of  light. 

The  reaction  of  the  pigment  layer  of  the  choroid  is  slight, 
as  most  of  the  energy  is,  as  it  were,  transmuted  from  the 
physical  into  nervous  energy,  which  is  equivalent  to  absorp- 
tion by  non-sensitive  dark  surfaces  when  a  real  image  is  cast 
upon  it.  But  reaction  is  sufficient,  nevertheless,  to  provide  a 
system  of  emergent  pencils  by  which  the  skiascopist  determines 
the  dioptric  error.  The  reaction  of  this  surface  is  analogous  to 
reflection,  but  as  each  pencil's  energy  is  confined  to  a  limited 
area — the  area  of  the  diffusion  circle  produced  by  it — there  is 
not  that  dissociation  of  impulses  from  many  pencils  and  reasso- 
ciation  such  as  we  have  from  rough  surfaces,  and  which  make 
the  surface  or  object  visible.  Each  circle  of  diffusion  contains 
the  energy  of  a  limited  area  of  the  light  and  gives  back  energy 
of  the  same  identity.  At  least  it  is  only  mixed  to  the  extent 
of  the  overlapping  of  diffusion  circles.  The  case  is  different  if 
a  screen  is  required  through  which  the  image  may  be  seen 
from  the  opposite  side,  as  the  ground  glass  field  used  in  the 
artist's  camera.  There  a  surface  is  required  that  will  transmit 
the  energy,  but  react  sufficiently  to  display  the  image. 

4.      THE    OBSERVING    EYE. 

This  is  the  subjective  area — objective,  however,  to  the 
observer's  higher  intellectual  faculties.    It  is  the  area  at  which 


STATIC    FACTORS    OF   SKIASCOPY.  121 

is  revealed  the  condition  of  the  dioptric  media  of  the  observed 
eye — the  ".v"  or  unknown  quantity  in  an  algebraic  equation 
all  of  whose  other  terms  are  known.  The  observer  formulates 
the  equation  in  his  examination,  and  then  he  has  but  to  reduce, 
simplify,  transpose,  eliminate  and  divide  by  the  coefficient  of 
"x"  to  determine  its  value  and  solve  the  problem.  The  observ- 
ing eye  occupies  the  same  relation  to  the  retinal  reflex  as  R 
and  R'  in  Fig.  23,  Chapter  III,  has  to  the  arrow  C  D,  whose 
virtual  image  appears  in  the  concave  mirror.  The  questions 
that  present  themselves  successively  to  the  skiascopist  in  an 
examination  with  a  plane  mirror  are  as  follows: 

1.  What  is  the  character  of  the  pencils  of  light  emitted  by 
the  observed  eye  from  the  image  upon  its  retina?  Are  they 
positive,  consisting  of  convex  waves;  are  they  neutral,  con- 
sisting of  plane  waves,  or  are  they  negative,  consisting  of  con- 
cave waves? 

2.  If  they  are  positive  or  negative  they  can  be  neutralized, 
a  positive  lens  neutralizing  positive  pencils,  and  a  negative 
lens  neutralizing  negative  pencils;  but  the  first  work  is  not  to 
neutralize  them,  but  make  them  of  a  fixed  concave  curvature — 

—  I  Cm. — or  to  focus  them  at  one  meter.  It  may  require  a 
plus  lens  to  do  this,  or  it  may  require  a  minus  lens. 

3.  The  skiascopist  determines  at  the  first  glance  which 
sort  of  lens,  plus  or  minus,  is  required  by  noting  whether  the 
retinal  reflex  or  image  moves  zvith  or  against  the  mirror  or 
"light  on  the  face."  If  it  moves  with  the  mirror  a  plus  lens  is 
required;  if  against  it,  a  minus  lens  is  necessary. 

4.  The  power  of  the  lens  is  determined  by  trial,  but  the 
power  is  indicated  by  the  rapidity  of  motion  of  the  reflex.  If  it 
moves  very  rapidly,  but  a  slight  increase  of  power  is  called 
for — the  more  rapidly  it  moves,  short  of  reversal,  the  nearer 
the  approach  to  the  point  desired.  Complete  elimination  of 
motion,  or  motion  so  rapid  or  instantaneous  that  direction  of 
motion  cannot  be  told,  completes  the  primary  correction. 

5.  The  above  brings  the  image  or  area  of  reversal  to  the 
eye  of  the  observer.  The  waves  of  the  emitted  pencils  are  —  i 
Cm.,  for  they  focus  at  one  meter.    It  is  only  necessary  to  add 

—  I  D.  to  the  primary  correction  to  neutralize  the  emergent 


122  STATIC    FACTORS    OF    SKIASCOPY. 

pencils.  If,  with  this  full  correction,  the  eye,  with  passive 
accommodation,  emits  neutral  pencils  of  light  from  an  image 
upon  its  retina,  it  w^ill  focus  neutral  pencils  or  pencils  from  the 
distant  object  at  the  retina. 

6.  If  different  meridians  of  the  eye  are  different,  it  is  only 
necessary  to  find  the  correction  for  each  of  the  principal  merid- 
ians and  prescribe  a  compound  lens  having  the  requisite  power 
in  each  meridian. 

It  would  seem,  from  the  above,  as  though  area  4  had  little 
to  do  with  the  examination,  except  as  it  revealed  the  condition 
of  area  3;  but  let  us  see.  When  a  lens  is  put  in  front  of  the 
observed  eye,  or  the  power  of  such  a  lens  is  changed,  the  waves 
of  the  incident  pencils  from,  the  luminous  area  undergo  modifi- 
cation. The  lens  either  assists  the  eye  in  doing  its  work  or 
increases  the  work  it  has  to  do.  This  afTects  the  retinal  image 
— increasing  or  decreasing  diffusion, — but  it  does  not  reverse 
the  motion  of  the  image  on  area  3.  That  is  always  the  same 
way — with  the  mirror.  The  rapidity  of  motion  at  area  3  is 
not  materially  affected,  whatever  the  lens  before  the  eye.  Re- 
versal of  motion  and  rapidity  of  motion,  or  change  of  rapidity 
of  motion,  are  phenomena  that  pertain  to  area  4  exclusively. 
The  appearance  of  reversal  and  change  of  motion  in  the  pupil 
of  the  observed  eye  is  due  to  the  principle  of  projection.  Re- 
versal of  motion  is  an  "optical  illusion,"  so-called,  and  like  all 
optical  illusions,  it  is  explainable  on  simple  optical  principles. 
Reversal  of  motion  on  area  4  is  due  to  transposition  of  the 
emergent  pencils  from  the  observed  eye  anterior  to  the  observ- 
ing eye  or  anterior  to  a  fixed  plane  in  the  observing  eye,  at 
which  the  transformation  occurs,  and  which  we  have  assigned 
as  the  plane  of  the  pupil.  If  the  real  image  anterior  to  the 
observed  eye  is  anterior  to  this  fixed  plane  in  the  observing 
eye,  inversion  and  reversal  of  motion  at  area  4  result.  If  it  is 
posterior  to  this  fixed  plane,  neither  inversion  nor  reversal  of 
motion  occur.  If  it  is  at  this  fixed  plane  the  image  is  lost,  and 
motion  or  the  direction  of  motion  is  indeterminate.  It  does 
not  matter  so  much  where  that  fixed  plane  in  the  observing 
eye  may  be,  but  the  phenomena  of  reversal  and  inversion, 
which  appear  at  the  retina  and  are  sensatory,  are  the  important 


STATIC    FACTORS    OF   SKIASCOPY  I23 

elements.  Our  reason  for  assigning  the  location  of  the  fixed 
plane  of  reversal  in  the  observing  eye  at  the  pupil  is  this:  The 
pupil  is  the  gateway  separating  the  outer  eye  and  the  world 
from  the  inner  eye.  through  which  all  pencils  pass.  It  is  similar 
to  the  door  of  a  church  through  which  people  are  passing  in 
or  out,  and  the  foci  of  the  pencils  are  crowded  more  closely 
together  there  than  at  any  other  point — not  because  of  the 
action  of  the  cornea,  but  because  of  the  lens  action  of  the 
observed  eye  in  focusing  the  pencils  at  the  pupil.  From  this 
plane  the  pencils  expand  on  either  side,  the  same  as  the  people 
within  or  without  the  church  doorway,  and  diffusion  at  the 
retina  is  then  at  the  maximum,  the  lens  having  little  effect  in 
condensing  or  focusing  tli'e  pencils  from  a  point  so  near  its 
anterior  surface,  especially  since  the  cornea,  at  this  point, 
gives  it  no  assistance. 

When  the  image  is  at  the  fixed  plane  of  reversal  in  the 
observing  eye,  no  image  appears  on  the  retina.  All  is  lost  in 
diffusion  at  area  4.  But  on  account  of  aberration,  certain  areas 
of  the  pupil  will  appear  illuminated  and  others  less  so,  because 
the  area  of  reversal  is  not  quite  the  same  for  different  pupillary 
spaces.  But  at  the  slightest  motion  or  quiver  of  the  hand 
these  illuminated  spaces  vanish,  though  in  what  direction  can- 
not be  told.  They  appear  to  consume  themselves,  or  the  darker 
areas  to  consume  the  areas  of  light.  A  slight  change  in  the 
power  of  the  lens  or  position  of  the  observing  eye  brings  up 
the  illumination  and  motion  again.  In  bringing  the  area  of 
reversal  to  the  fixed  plane  of  reversal,  the  area  of  reversal  in 
the  observing  eye,  and  not  the  exterior  aerial  image  or  area 
of  reversal,  is  considered.  When  the  aerial  or  potential  image 
is  posterior  to  the  observing  eye,  the  area  of  reversal  or  image 
in  the  eye  is  anterior  to  the  retina  but  posterior  to  the  fixed 
plane  of  reversal.  As  the  area  of  reversal  within  the  observing 
eye  is  brought  forward  toward  the  fixed  plane  of  reversal  by  a 
stronger  plus  lens  or  the  area  of  reversal  or  image  anterior  to 
the  observing  eye  is  brought  back  by  a  stronger  minus  lens, 
motion  becomes  more  rapid.  As  the  area  of  reversal  ap- 
proaches the  fixed  plane  the  image  grows  less  and  less  distinct, 
■  although  illumination  increases,  on  account  of  increasing  dif- 
fusion; but  such  imperfect  image,  with  the  slightest  motion  of 


124  STATIC    FACTORS    OF   SKIASCOPY. 

the  mirror,  sweeps  across  the  entire  retinal  field  or  field  of 
vision  on  which  it  is  displayed.  To  reverse  motion  it  is  neces- 
sary that  the  area  of  reversal  cross  the  fixed  plane  of  reversal 
of  the  observing-  eye. 

Tlie  efifect  at  area  4  depends  upon  the  sort  of  waves  of 
which  the  emitted  pencils  are  composed;  and  what  those  waves 
are  depends  upon  the  dioptric  power  of  the  observed  eye  com- 
pared with  the  distance  of  its  retina  from  the  dioptric  media. 
If  the  emitted  pencils  consist  of  convex  waves,  they  have  no 
anterior  foci,  nor  is  there  an  anterior  image.  The  dioptric 
media  has  not  sufftcient  power  and  requires  a  positive  lens  to 
supplement  it.  But  the  observing-  emmetropic  eye  is  able  to 
focus  these  convex  waves  by  the  use  of  a  sufficient  degree  of 
its  accommodation.  If  the  emitted  pencils  are  neutral  or  con- 
sist of  plane  waves,  the  eye's  accommodation  being-  passive, 
its  dioptric  media  is  exactly  adapted  to  the  distance  of  the 
retina  from  which  the  pencils  come.  It  will  not  focus  pencils 
from  a  finite  distance  upon  the  retina,  for  an  emmetropic  eye 
with  passive  accommodation  is  not  supposed  to  do  that;  it 
would  not  be  emmetropic  if  it  did.  Tlie  emitted  neutral  pencils 
have  no  anterior  focus,  but  the  observing  emmetropic  eye  will 
focus  them  without  the  use  of  its  accommodation.  If  the 
emitted  pencils  are  composed  of  concave  waves,  then  each 
pencil  has  a  potential  or  actual  focus  anterior  to  the  eye — a 
center  of  curvature  for  these  negative  waves.  Together  these 
foci  make  the  anterior  image  or  area  of  reversal.  The  aerial 
image  or  area  of  reversal  may  be  posterior  to  the  observing 
eye,  but  the  area  of  reversal  within  the  observing  eye,  in  that 
case,  is  anterior  to  the  retina,  but  posterior  to  the  fixed  plane 
of  reversal.  If  the  area  of  reversal  is  anterior  to  the  fixed  plane 
of  reversal,  which  it  would,  of  course,  be  if  anterior  to  the 
cornea,  and  might  be  if  slightly  posterior  to  it,  motion  against 
the  mirror  results. 

The  observing  eye  may  thus  receive  either  of  three  kinds 
of  waves:  (i)  convex  waves,  (2)  neutral  waves,  or  (3)  con- 
cave waves.  The  first  class  may  be  those  evolved  at  area  3, 
which  the  dioptric  media  of  the  observed  eye  has  been  unable 
to  transpose,  or  it  may  be  the  convex  waves  evolved  at  an 
area  of  reversal  anterior  to  the  observing  eye,  which  would 


STATIC    FACTORS    OF   SKIASCOPY.  I25 

invert  the  entire  group  of  pencils  and  each  individual  pencil  of 
the  group.  If  the  waves  are  of  the  former  class — convex  w^aves 
evolved  at  area  3  and  unneutralized  by  the  dioptric  media  of 
the  observed  eye — their  curvature  will  be  comparatively  slight 
and  the  dioptric  media  of  the  observing  eye,  with  slight  use 
of  its  dynamic  power,  will  be  able  to  focus  them  upon  the 
retina.  It  will  also  focus  neutral  waves  without  the  use  of  its 
accommodation.  This  leaves  the  two  important  classes  of 
waves  in  skiascopy  yet  to  be  disposed  of:  (i)  convex  waves 
that  are  evolved  at  an  area  of  reversal  between  the  observed 
and  observing  eye,  and  (2)  concave  waves. 

If  the  waves  are  concave  their  potential  foci  are  posterior 
to  the  observing  eye,  and  the  area  of  reversal  in  the  observing 
eye  will  be  forward  of  the  retina,  and  there  will  be  diffusion  at 
the  retina.  The  emmetropic  observing  eye  cannot  focus  these 
pencils,  either  with  or  without  its  accommodation.  Thf  farther 
forward  such  area  of  reversal  is  from  the  retina,  up  to  the  fixed 
plane  of  reversal,  the  greater  its  incapacity  to  focus  the  pencils 
and  the  greater  the  diffusion  at  the  retina.  But  when  the  area 
of  reversal  has  crossed  the  fixed  plane,  then  the  eye  has  reached 
and  passed  the  fullness  Of  its  incapacity,  and  the  farther  for- 
ward the  area  of  reversal  moves  the  more  potent  the  observing 
eye  becomes.  In  passing  out  of  the  eye  and  into  space  between 
the  two  eyes  the  waves  at  the  cornea  become  convex,  for  the 
centers  of  curvature  of  all  pencils  are  anterior  to  it.  But  the 
group  of  pencils,  and  each  pencil,  is  inverted,  and  there  is  a 
real  image  in  front  of  the  cornea  of  the  observing  eye.  Whether 
the  observing  eye  can  focus  these  transposed  and  inverted 
pencils  depends  upon  the  convexity  of  the  waves  or  the  near- 
ness of  the  aerial  image.  It  cannot  focus  them  if  such  image 
is  nearer  than  its  punctum  proximum,  although  it  will  obtain 
an  imperfect  or  diffuse  image — a  sufficiently  clear  image  to 
■Bee  motion — very  soon  after  the  area  of  reversal  emerges  from 
the  eye. 

Whatever  the  class  of  waves  that  come  to  the  observing 
eye,  it  cannot  escape  diffusion  at  the  retina,  even  when  it 
focuses  the  emitted  pencils  exactly,  for  there  is,  in  that  case, 
diffusion  at  area  3,  and  the  observing  eye  focuses  accurately 
the  pencils  emitted  from  this  diffuse  image.     The  picture  on 


126  STATIC    FACTORS    OF    SKIASCOPY. 

area  4  is  not  a  good  one,  not  because  the  emitted  pencils  are  not 
all  right,  nor  because  the  observing  eye  cannot  focus  them, 
but  because  the  observed  eye,  which  emits  these  acceptable 
pencils,  has  a  diffuse  image  at  its  retina,  and  the  image  at  area 
4  cannot  be  better  than  its  original.  But  if  the  image  at  area  3 
is  exact  for  a  luminous  object  at  a  finite  distance,  it  is  trans- 
posing positive  into  negative  waves — doing  anterior  and  pos- 
terior work  at  the  same  time.  The  emitted  pencils  will  there- 
fore consist  of  concave  waves,  and  these  the  emmetropic  ob- 
serving eye  cannot  focus  at  the  retina,  hence  diffusion  at  area  4 
in  spite  of  the  clear  image  at  area  3.  Diffusion  at  area  4  is 
unavoidable,  unless  the  incident  and  emergent  pencils  are 
reduced  to  one  kind.  This  could  be  done  only  by  neutralizing 
the  incident  pencils  before  they  should  reach  the  observed  eye 
by  a  neutralizing  lens  in  the  skiascopic  chimney  or  otherwise. 
If  that  were  done  the  same  lens  that  neutralized  the  emergent 
pencils 'from  the  retina  would  focus  the  neutral  incident  pencils 
upon  the  retina. 

The  distinct  skiascopic  phenomena  at  area  4  are  inversion 
and  reversal  of  motion.  Inversion  is  the  static  and  reversal  of 
motion  the  dynamic  phenomenon.  Reversal  is  due  to  inver- 
sion, for  inversion  makes  the  retinal  images  the  same  in  both 
observed  and  observing  eyes,  and  projection  of  the  image  at 
area  4  is  the  inverse  of  the  image  at  area  3,  although  the  two 
images  are  the  same— the  inverse  of  the  object.  But  the  static 
effect  is  not  easily  seen  on  account  of  diffusion.  Even  if  the 
figure  of  the  luminous  area  were  distinctive,  as  that  of  a 
triangle,  apex  upward,  diffusion  would  tend  to  obliterate  its 
form.  But  motion  in  an  opposite  direction  from  the  motion  of 
the  mirror,  or  with  it,  is  not  easily  mistaken.  These  reverse 
motions  may  be  obtained  by  a  difference  of  .25  D.  in  the  lens 
power,  showing  that  the  area  of  reversal  has  crossed  the  fixed 
plane,  giving  these  opposite  effects  at  area  4. 

SUBSIDIARY  AREAS. 

We  have  noted  some  of  the  subsidiary  areas,  as  :  (i)  the 
area  of  reversal  or  focal  area,  (2)  the  fixed  plane  of  reversal  in 
the  observ'ing  eye,  (3)  the  focal  area  in  the  observed  eye  or 
posterior  to  it.    If  a  concave  mirror  is  used  there  is  (4)  a  focal 


STATIC    FACTORS    OF   SKIASCOPY.  127 

area  between  the  mirror  and  observed  eye,  which  is  an  area 
of  reversal  or  inversion,  or  transposition  of  the  incident  pencils. 
It  reverses  all  of  the  phenomena  pertaining  to  the  skiascopic 
tests  with  a  plane  mirror.  If  the  concave  mirror  of  +  4  D. 
■or  focal  length  of  10  in.  or  25  centimeters — the  usual  power  of 
a  concave  skiascopic  mirror — is  used  and  the  luminous  area 
is  one  meter  from  the  mirror,  i  D.  of  its  power  is  required  to 
neutralize  the  pencils,  leaving  -r  7,1).  for  focal  purposes,  which 
places  the  image  13  in.  or  33  centimeters  from  the  mirror.  If 
the  examination  distance  is  one  meter,  the  immediate  source  of 
the  pencils  of  light  that  reach  the  observed  eye  will  be  i  meter 
—  13  in.  =  27  in.  or  67  centimeters  from  the  observed  eye.  At 
i:^  meters  the  immediate  source  of  light  is  nearly  i  meter  from 
the  observed  eye. 

THE  INTERVALS. 

The  intervals  between  the  areas  are  important  static  fac- 
tors, because  they  are  the  evolutionary  spaces — the  spaces  in 
which  the  waves  evolve  a  curvature  different  than  that  with 
which  they  start. 

I.     thj:  first  ixter\^\l. 

This  extends  from  the  luminous  area  (area  i)  to  the 
mirror  (area  2).  If  the  luminous  ajea  is  a  lamp  or  gas  flame, 
the  flame,  and  not  the  chimney  that  encloses  it,  is  the  luminous 
area.  But  if  a  diffusion  disc  is  between  the  flame  and  the 
mirror,  tlie  interval  is  the  distance  of  such  disc  from  the  mirror, 
for  a  diffusion  disc  reforms  the  waves  of  all  pencils  and  be- 
comes a  new  center  for  such  pencils.  The  curvature  evolved 
by  the  waves  in  interval  i  depends  upon  its  length.  If  it  is  i 
meter  the  waves  evolve  a  curature  of  +  i  Cm.,  if  it  is  10  in.  the 
waves  evolve  a  curvature  of  4-  4  Cm.  The  plane  mirror  does 
not  modify  such  curvature,  whatever  it  may  be.  It  simply 
changes  the  direction  of  the  waves  which  continue  to  evolve  a 
different  curvature  as  before.  If  a  neutralizing  lens  is  placed 
so  as  to  intercept  and  neutralize  all  pencils  from  the  luminous 
area,  as  a  +  10  D.  lens  4  m.  from  the  flame,  the  waves  of  every 
pencil  become  static  in  curvature,  or  would  but  for  aberration. 
Distance  would  increase  aberration,  but  would  have  no  effect 
upon  neutral  waves — that  is,  in  modifying  their  curvature,  as 


128  STATIC    FACTORS    OF    SKIASCOPY. 

they  would  have  no  curvature  to  modify.  A  T-chimney  with 
such  a  neutralizing  lens  in  it  that  could  be  accurately  adjusted 
would  undoubtedly  offer  some  new  skiascopic  data  of  value. 
The  lens  should  be  less  than  neutralizing  rather  than  more,  for 
then  evolution  would  tend  still  further  to  neutralize  the  waves, 
while  if  the  lens  transposed  the  waves,  evolution  would  in- 
crease their  concavity. 

2.      THE   SECOND    INTERVAL. 

The  second  interval  consists  of  two  parts,  (i)  the  distance 
from  the  mirror  to  the  cornea  of  the  observed  eye,  and  (2)  the 
distance  of  the  cornea  from  the  retina.  The  former  is  the 
evolutionary  space,  for  there  only  the  waves  are  in  homogene- 
ous air.  As  the  evolution  of  the  waves  in  interval  2  is  but  a 
continuation  of  evolution  in  interval  i,  intervals  i  and  2  count 
as  one  in  the  evolution  of  the  waves  from  the  luminous  area  to 
the  cornea  of  the  observed  eye.  The  two  intervals  are  taken 
together  in  determining  the  distance  of  the  luminous  area  from 
the  observed  eye. 

3.      THE    THIRD    INTERVAL. 

This  is  again  the  subjective  interval — the  interval  that  ends 
at  the  subjective  area.  It  is  the  space  between  the  observed 
and  observing  eye.  The  evolutionary  space  is  from  cornea  to 
cornea,  or  from  the  glass  in  front  of  the  observed  eye  to  the 
cornea  of  the  observing  eye.  The  entire  interval  consists,  then, 
of  the  space  from  area  3  to  the  cornea  of  the  observed 
eye,  the  space  from  the  cornea  of  the  observed  eye  to  the 
cornea  of  the  observing  eye,  and  the  space  from  the  cornea 
of  the  observing  eye  to  area  4.  The  first  and  last  of  these 
spaces  are  inconsiderable  and  unimportant.  The  dioptric 
media  is  supposed  to  take  care  of  them,  and  if  it  does  not,  there 
is  no  way  of  correcting  its  defects  except  upon  the  outside. 
But  interval  2  and  interval  3  are  almost  identical,  since  the 
observing  eye  is  just  posterior  to  the  mirror.  They  might  be 
considered  as  identical  if  anything  was  to  be  gained  by  it;  but 
it  is  really  the  sum  of  intervals  i  and  2,  rather  than  2  alone, 
that  is  the  important  incident  space,  and  this  is  always  greater 
with  a  plane  mirror  than  interval  3.     It  is  greater  with  any 


STATIC    FACTORS    OF   SKIASCOPY.  I29 

kind  of  a  mirror,  but  with  a  concave  mirror  the  sum  of  intervals 

1  and  2  divides  into  two  parts — (i)  the  part  from  the  luminous 
area,  by  way  of  the  mirror,  to  the  focal  area  in  front  of  the 
mirror,  and  (2)  the  part  from  the  focal  area  in  front  of  the 
mirror  to  the  cornea  of  the  observed  eye.  The  last  is  the  real 
evolutionary  space,  and  it  is  necessarily  less  than  interval 

2  or  3. 

SUBSIDIARY   INTERVALS. 

We  have  already  referred  to  the  subsidiary  intervals, 
though  not  specifically.  They  are  (i)  the  space  from  the  lum- 
inous area  to  the  focal  area  of  a  concave  mirror,  (2)  the  space 
from  such  focal  area  to  the  cornea  of  the  observing  eye,  (3)  the 
space  from  the  cornea  of  the  observed  eye  to  the  area  of  re- 
versal when  anterior  to  the  observing  eye,  (4)  the  space  from 
such  area  of  reversal  to  the  cornea  of  the  observing  eye.  In 
any  and  all  of  the  intervals  the  force  of  evolution  alone  modi- 
fies the  curvature  of  the  waves.  There  are  minute  intervals — 
as  the  intervals  between  the  different  dioptric  surfaces,  but 
these  have  already  been  considered  in  the  chapter  on  the  re- 
fraction of  the  eye. 


CHAPTER  VI. 


DYNAMIC    FACTORS    OF    SKIASCOPY.       TILTING    MIRROR   AND    ITS 

DYNAMIC    EFFECTS.       MOTION    AT    LUMINOUS 

AREA.       CHANGING    THE    INTERVALS. 

OTHER  DYNAMIC   PRINCIPLES. 


SKIASCOPY  is  essentially  a  dynamic  method  of  ocular  ex- 
amination. It  has  its  static  factors,  for  dynamics  in  any 
department  of  physical  science  must  have  a  static  founda- 
tion. All  natural  phenomena  are  due  to  the  combination  of 
some  static  element  with  a  dynamic  force.  A  cannon-ball  mov- 
ing through  space  has  what  is  termed  a  "striking  force."  Its 
striking  force  is  equal  to  its  weight  multiplied  by  the  square  of 
its  velocity.  Its  motion  multiplied  by  its  velocity  alone  is  called 
its  momentum.  Hence  its  striking  force  is  its  m.omentum  mul- 
tiplied by  its  velocity  again.  We  have,  then,  in  its  striking 
force  the  product  of  tw^o  factors:  (i)  its  momentum,  and  (2)  its 
velocity.  Its  momentum  is  the  static  factor  of  striking  force, 
and  velocity  is  the  dynamic  factor. 

But  momentum  is  itself  a  compound,  for  it  is  the  weight 
of  the  cannon-ball  multiplied  by  its  velocity.  Momentum  is 
the  product  of  two  factors,  (i)  weight  and  (2)  velocity.  Its 
weight  is  the  static  factor,  and  its  velocity  is  the  dynamic 
factor.  But  weight,  the  static  factor  of  momentum,  is  a  com- 
pound, the  static  factor  of  which  is  its  quantity  of  matter  or 
mass,  and  the  dynamic  factor  of  which  is  the  force  of  gravity. 
Can  we  go  further?  Surely.  The  quantity  of  matter  in  the 
cannon-ball  is  compound,  embodying  extension  or  volume, 
which  is  due  to  molecular  motion,  heat,  which  tends  to  separate 
the  molecules,  and  cohesion,  or  the  attraction  between  these 
molecules,  tending  to  unite  them  more  closely.  We  have  gone 
some  distance  in  the  study  of  the  molecular  forces,  but  there 
are  undiscovered  principles  as  yet  far  beyond  our  reach. 

130 


DYNAMIC    FACTORS    OF    SKIASCOPV.  I3I 

I.      TILTING  THE   MIRROR. 

A  dynamic  principle  is  a  principle  that  manifests  itself  by 
force,  motion  or  action.  A  dynamic  effect  is  the  efifect  of  the 
operation  of  force.  Visually  it  manifests  itself  by  motion.  We 
have  seen,  in  Chapter  I,  how  the  tilting  of  the  mirror  produces 
dynamic  effects.  It  causes  the  incident  pencils  to  reach  the 
mirror  at  a  different  angle,  and  as  a  result  the  reflected  pencils 
pass  from  the  mirror  at  a  different  angle  and  in  a  different 
direction.  A  change  in  the  inclination  of  the  mirror  to  the 
incident  pencils  of  10°  produces  a  change  in  the  direction  of 
the  reflected  pencils  of  20°.  Change  of  direction  of  the  reflected 
pencils  is,  then,  a  dynamic  effect.  But  this  causes  the  area  of 
light  upon  which  the  reflected  pencils  fall  to  move,  as  from 
right  to  left  or  left  to  right,  upward,  downward  or  obliquely. 
That  is,  there  is  motion  of  the  "light  on  the  face."  But  this 
gives  rise  to  other  dynamic  effects.  The  minor  pencils  that 
enter  the  observed  eye  are  changed,  the  former  ones  passing 
off  to  be  succeeded  by  others  as  long  as  the  light  area  covers 
the  pupil.  But  as  the  new  minor  pencils  are  pursuing  a  differ- 
ent course  on  account  of  the  change  in  the  inclination  of  the 
mirror,  the  direction  from  which  they  come  or  reach  the  eye 
is  changed.  They  become  more  or  less  oblique  to  the  visual 
axis  of  the  observed  eye,  and  the  dioptric  media  focuses  them 
at  a  new  area,  either  at  the  retina  or  anterior  or  posterior  to 
it.  If  either  of  the  latter  the  diffusion  circles  at  the  retina  and 
the  imperfect  image  they  form  is  upon  a  different  retinal  area. 
The  newly  located  image  is  projected  in  a  different  direction, 
and  the  virtual  image  appears,  to  the  one  under  examination, 
to  move.  Nor  is  this  all.  The  image  of  the  luminous  area 
having  a  different  retinal  position  at  area  3,  the  pencils  from 
this  image  pursue  a  different  course  on  their  way  out  of  the 
observed  eye.  If  the  retinal  image  at  area  3  has  been  moved 
to  the  left,  the  emergent  pencils  must  take  a  direction  more 
to  the  right,  or  they  will  be  turned  back  by  the  iris.  This 
changes  the  direction  of  the  emergent  pencils  that  come  to  the 
perforation  in  the  mirror  and  to  the  observing  eye.  It  gets  a 
new  set  of  pencils  pursuing  a  slightly  different  general  direc- 
tion. This  places  the  image  at  area  4,  the  sensatory  subjective 
area,  in  a  new  position  on  the  retina.   It  projects  the  new  image 


132  DYNAMIC    FACTORS    OF    SKIASCOPY. 

in  a  different  direction.  And  thus  one  dynamic  effect  follows 
another.  The  mere  tilting  of  the  mirror  is  the  primary  cause 
of  all  these  changes. 

The  different  dynamic  effects  of  tilting  the  mirror,  all 
other  static  factors  remaining  stationary,  may  be  summed  up 
as  follows: 

1.  Change  of  angle  of  incident  pencils. 

2.  Change  of  direction  of  reflected  pencils. 

3.  Motion  of  "light  on  the  face." 

4.  Change  of  minor  pencils  entering  the  pupil  of  the  ob- 
served eye. 

5.  Change  of  direction  of  minor  with  the  major  pencils. 

6.  Change  of  location  of  image  on  area  3. 

7.  Change  of  direction  of  projection  of  image  on  area  3. 

8.  Change  of  direction  of  emergent  pencils  from  image 
on  area  3. 

9.  Change  of  pencils  reaching  perforation  and  observing 
eye. 

10.  Change  of  direction  of  such  pencils. 

11.  Change  of  position  of  image  on  area  4. 

12.  Change  of  direction  of  projection  of  such  image. 

This  is  a  list  of  dynamic  effects  that  seems  out  of  propor- 
tion to  the  cause,  but  the  history  of  the  world  and  of  nations, 
as  well  as  of  individuals,  is  made  up  of  chains  of  dynamic 
causes  and  effects,  on  the  same  principle.  They  do  not  stop 
where  we  have  stopped.  There  were  preceding  dynamic 
causes,  and  there  will  be  succeeding  dynamic  effects,  although 
these  comprise  those  that  are  distinctively  optical. 

2.       CHANGE   OF  DIOPTRIC   POWER. 

If  the  observed  eye,  which  has  the  power  of  accommoda- 
tion supposed  to  be  passive  during  a  skiascopic  examination, 
should  exercise  its  dynamic  power,  as  by  using  or  putting 
forth  2  D.  of  accommodation  Vv^hile  under  examination,  the 


DYNAMIC    FACTORS    OF   SKIASCOPY.  I33 

dynamic  effects  would  be  varied  and  striking.  Suppose  an 
emmetropic  eye,  being  examined  from  one  meter  with  a  plane 
mirror,  the  luminous  area  being  one  meter  from  the  mirror 
or  two  meters  from  the  observed  eye,  should  put  forth  that 
power,  all  other  dynamic  causes  being  passive  or  quiet.  To 
appreciate  the  dynamic  effects  we  must  consider  the  results  of 
both  static  conditions — that  is,  with  the  accommodation  pas- 
sive and  with  the  accommodation  active. 

1.  With  passive  accommodation  the  incident  pencils  of 
"+  .5  Cm.  would  have  the  potential  foci  posterior  to  area  3,  and 
on  area  3  there  would  be  an  imperfect  image  produced  by  diffu- 
sion circles.  But  the  pencils  emitted  from  this  image  on  the 
retina  would  be  neutral,  and  as  neutral  waves  the  light  would 
pass  from  the  observed  to  the  observing  eye.  The  observ- 
ing eye,  wdth  passive  accommodation,  would  focus  these  neu- 
tral pencils  upon  area  4,  but  the  image  would  be  no  better  than 
its  original — the  image  produced  by  diffusion  circles  at  area  3. 
This  image  it  would  project  into  the  pupil  of  the  observed  eye. 

2.  With  2  D.  of  its  accommodation  in  force,  the  dioptric 
media  of  the  observed  eye  would  transpose  the  waves  of  the 
incident  pencils,  focusing  them  forward  of  the  retina,  as  its 
dioptric  power  would  be  1.5  D.  in  excess  of  that  required  to 
focus  -1-  .5  Cm.  waves  at  the  retina.  The  image  at  the  retina  or 
at  area  3  would  be  imperfect  because  produced  by  diffusion 
circles  from  a  focal  area  anterior  to  the  retina.  But  the  emerg- 
ent pencils  would  be  emitted  in  concave  waves — waves  that 
would  have  a  curvature  of  —  2  Cm.,  and  therefore  focus  ^ 
meter  anterior  to  the  cornea  of  the  observed  eye,  where  there 
would  be  a  true  image — the  so-called  area  of  reversal.  But 
this  area  of  reversal  would  be  anterior  to  the  observing  eye 
also.  Hence  all  the  pencils  that  reached  it  would  have  been 
transposed  and  inverted  at  such  area  of  reversal.  The  observ- 
ing eye  would  require  2  D.  of  its  accommodation  to  focus  these 
pencils,  and  the  image  at  area  4,  though  exact  as  to  the  image 
at  area  3,  would  duplicate  the  effects  produced  at  area  3  by 
diffusion.  But  the  image  at  area  4  would  be  the  same  in  posi- 
tion as  the  image  at  area  3 — that  is,  since  the  image  at  area  3 
is  inverted,  but  would  be  projected  as  erect,  and  there  is  an 


134  DYNAMIC   FACTORS    OF   SKIASCOPY. 

inversion  of  that  image  anterior  to  the  observing  eye,  which 
image  is  erect,  the  re-inversion  of  such  erect  image  would  pro- 
duce an  inverted  image  at  area  4  the  same  as  at  area  3,  which 
would  be  projected  as  erect. 

To  more  clearly  show  the  two  static  conditions  we  will 
suppose  the  mirror  to  be  tilted  in  each  case.  In  the  first  case 
the  motion  of  the  image  is  with  the  mirror,  because  the  image 
on  area  4  is  the  reverse  or  inverse  of  the  image  on  area  3, 
and  motion  of  the  image  to  the  right  on  area  3  is  motion 
to  the  left  on  area  4.  But  the  projection  of  such  motion 
is  to  the  right  or  with  the  motion  of  the  image  at  area  3. 
In  the  second  case  motion  to  the  right  of  the  image  on  area  3 
produces  motion  to  the  left  of  the  aerial  image  between  the 
observed  and  observing  eyes.  But  motion  to  the  left  of  the 
aerial  image  produces  motion  to  the  right  of  the  retinal  image 
at  area  4 — the  same  as  at  area  3.  But  projection  causes  such 
motion  to  be  to  the  left  or  with  the  aerial  image.  Hence 
motion  in  the  pupil  of  the  observed  eye  appears  to  be  contrary 
to  real  motion  there. 

Now  we  are  to  consider  the  effects  of  the  observed  eye 
changing  from  one  of  these  conditions  to  the  other  by  putting 
forth  its  dynamic  power.  The  exercise  of  this  power  requires 
change  or  motion.  The  ciliary  muscle  contracts,  the  choroid 
coat  is  pulled  forward,  the  tension  on  the  suspensory  ligament 
relaxes,  the  elasticity  of  the  lens  is  relieved  of  restraint,  and 
the  lens  expands  its  surfaces,  particularly  the  anterior  surface, 
become  more  curved,  and  the  lens  power  is  increased.  The 
incident  pencils  do  not  feel  the  influence  of  the  eye's  increased 
power  until  they  reach  the  anterior  surface  of  the  lens.  Then 
the  positive  refraction  of  that  surface  is  augmented,  while  the 
effect  at  the  posterior  surface  is  slightly  increased.  Under 
these  influences,  if  the  dynamic  power  is  put  forth  gradually, 
the  focal  area  or  potential  focal  area  posterior  to  the  retina 
begins  to  advance  toward  the  retina,  but  this  effect  is  not  real. 
The  real  effect  at  the  retina  is  that  the  diffusion  circles  contract 
and  the  image  becomes  more  distinct,  until  ^  D.  of  dynamic 
power  is  in  force,  when  diffusion  is  eliminated  at  the  retina. 
The  image  becomes  clear  and  sharp.  But  as  more  dynamic 
power  is  added,  the  focal  area  advances  and  positive  diffusion 


DYNAMIC    FACTORS    OF    SKIASCOPY.  135 

begins  to  become  manifest.  As  the  increase  of  dynamic  power 
goes  on  the  focal  area  advances  and  diffusion  at  the  retina 
grows  until  the  full  2  D.  is  in  force. 

Now,  while  these  changes  in  the  retinal  image  at  area  3 
are  taking  place,  the  emitted  pencils,  which  consisted  of  neutral 
waves,  become  concave  and  form  a  focal  area  anterior  tO'  the 
observed  eye  and  posterior  to  the  observing  eye.  But  within- 
the  observing  eye,  at  area  4,  there  was,  with  passive  accom- 
modation in  the  observed  eye.  correctly  focused  pencils  upon 
area  4.  But  with  the  transmission  of  concave  waves  to  the 
observing  eye  its  capacity  to  focus  the  pencils  at  the  retina 
ceases.  The  focal  area  advances,  and  when  the  focal  area  in 
the  observed  eye  is  at  area  3  and  the  clearest  image  appears, 
at  area  4  there  is  diffusion  because  of  the  over-power  of  the 
dioptric  media  of  the  observing  eye,  for  these  emitted  concave 
waves.  With  the  advance  of  the  focal  area  in  the  observed 
eye  the  focal  area  or  area  of  reversal  in  the  observing  eye  ad- 
vances still  farther,  and  diffusion  grows  at  area  4  because  of 
the  eye's  over-power.  It  recjuires  but  the  use  of  i  D.  of  the 
observed  eye's  accommodation  to  bring  the  area  of  reversal 
in  the  observing  eye  to  the  fixed  plane  of  reversal,  at  which 
point  all  the  peculiar  effects  noted  when  that  position  is  reached 
appear.  Diffusion  is  at  the  maximum  on  area  4,  and  no  image 
appears,  for  this  is  the  plane  of  transition,  and  the  crossing  of  it 
by  the  area  of  reversal  reverses  motion  and  inverts  the  image 
at  area  4.  By  the  advance  of  the  area  of  reversal  in  the  ob- 
serving eye  it  passes  successively  (i)  the  center  of  curvature 
of  the  anterior  surface  of  the  lens,  (2)  the  center  of  curvature 
of  the  cornea,  (3)  the  posterior  surface  of  the  lens,  (4)  the 
anterior  surface  of  the  lens,  (5)  the  center  of  curvature  of  the 
posterior  surface  of  the  lens,  and  (6)  the  cornea.  The  refracting 
surfaces,  which  are  in  natural  vision  all  positive  in  their  action, 
become  negative  when  the  waves  acquire  a  curvature  con- 
forming with,  but  greater  than,  the  curvature  of  the  refracting 
surface.  The  advance  of  the  area  of  reversal  is  not  a  steady 
advance,  for  when  a  refracting  surface  begins  to  act  negatively 
it  delays  the  advance  of  the  focal  area.  The  anterior  surface  of 
the  lens  is  first  to  become  negative,  but  it  becomes  positive 
again  as  soon  as  the  focal  area  passes  in  front  of  it.     The 


136  DYNAMIC   FACTORS    OF   SKIASCOPY. 

posterior  surface  becomes  negative  when  the  focal  area  crosses 
it,  and  remains  negative  until  the  positive  refraction  of  the 
anterior  surface  gives  it  waves  of  less  curvature  than  itseff. 
The  cornea  is  last  to  become  negative  in  its  action  and  last  to 
become  positive  again. 

The  focal  area  thus  advances  and  is  delayed  or  lingers  at 
a  fixed  position  or  near  it,  then  going  forward  rapidly  for  a 
space  to  be  delayed  again,  until  it  passes  out  of  the  eye  at  the 
cornea  and  all  the  surfaces  become  positive.  When  the  ob- 
served eye  is  exercising  i  D.  of  its  dynamic  power,  or  the  least 
trifle  over  i  D.,  the  focal  area  or  area  of  reversal  emerges  from 
the  observing  eye.  During  all  the  preceding  advances  diffu- 
sion at  area  4  has  increased,  but  with  the  passing  of  the  area 
of  reversal  across  the  fixed  plane  of  reversal  diffusion  begins 
to  lessen.  When  the  focal  area  is  tangent  to  the  cornea  diffu- 
sion is  great,  for  this  position  is  reached  by  the  focal  area 
almost  instantly  after  passing  the  fixed  plane.  Every  pencil  is 
composed  of  convex  waves  of  such  high  curvature  that  the 
dioptric  media,  though  acting  in  that  direction,  are  quite  unable 
to  focus  them  upon  tfie  retina,  and  continue  to  be  unable  to 
do  so  until  the  focal  area  reaches  the  punctum  proximum  of 
the  observing  eye.  Diffusion  grows  less,  however,  as  the  focal 
area  advances,  and  from  the  punctum  proximum  to  the  posi- 
tion -J  meter  in  front  of  the  observing  eye  less  and  less  of  its 
accommodation  is  used.  It  does  not,  however,  get  a  good 
definition  of  the  luminous  area,  although  it  focuses  the  emitted 
pencils  accurately,  because  of  diffusion  at  area  3. 

If  during  the  transition  of  the  focal  area  from  the  retina 
of  the  observing  eye  to  a  position  ^  meter  in  front  of  it 
the  other  dynamic  cause,  tilting  the  mirror,  were  applied,  all 
the  skiascopic  phenomena  would  appear.  As  the  area  of  re- 
versal passed  the  fixed  plane,  motion  would  he  reversed  from 
zvith  the  mirror  to  against  it.  At  the  fixed  plane  the  image, 
as  such,  would  disappear.  Approach  of  the  area  of  reversal 
to  the  fixed  plane  would  cause  motion  to  grow  more  and  more 
rapid,  but  the  advance  of  the  area  of  reversal  from  the  fixed 
plane  would  show  the  most  rapid  motion  when  reversal  of  mo- 
tion first  appeared,  and  it  would  grow  less  rapid  in  the  same 
degree  that  diffusion  at  area  4  lessened.  The  cause  for  all  these 


DYNAMIC   FACTORS    OF   SKIASCOPY.  I37 

peculiar  skiascopic  phenomena  have,  we  think,  been  made 
clear. 

3.       CHANGING    THE    INTERVALS. 

But  the  use  of  the  accommodation  of  the  observed  eye  to 
bring  about  these  effects  is  a  suppositional  case  merely.  It  is 
not  a  practical  skiascopic  method.  But  the  same  effects,  or 
corresponding  effects,  are  produced  in  practical  skiascopy  by 
two  other  means:  (i)  changing  the  length  of  the  intervals  dur- 
ing an  examination,  and  (2)  putting  plus  lenses  before  the 
observed  eye.  These  are  the  two  means  the  skiascopist  con- 
stantly employs,  especially  the  latter,  for  that  is  the  purpose 
of  the  examination:  To  determine  the  lens  required  to  make 
the  eye  artificially  emmetropic.  We  will  look  at  these  two 
dynamic  factors  separately,  and  determine  certain  limitations 
by  which  they  are  bounded. 


The  three  intervals  are  peculiarly  associated  with  one 
another.  An  interval  is  shortened  or  lengthened  by  changing 
the  position  of  one  or  more  of  the  areas.  Now,  if  while  areas  2, 
3  and  4  are  unchanged,  area  i  is  brought  nearer  to  or  moved 
farther  from  area  2,  the  first  interval  alone  is  altered.  It  is 
altered  the  exact  amount  of  the  changed  position  of  area  i. 
If,  for  instance,  area  i  is  moved  from  a  position  of  i  m.  from 
area  2  to  a  position  of  i  meter,  interval  i  is  reduced  -J  meter, 
as  shown  in  Fig.  36.  But  as  the  incident  pencils  are  evolved 
through  the  space  of  intervals  i  and  2  combined,  shortening 
interval  i  reduces  this  evolutionary  space  ^  meter.  If  intervals 
I  and  2  are  each  i  meter,  the  reduction  of  interval  i  to  ^  meter 
reduces  the  entire  space  from  2  meters  to  i^  meters,  and  the 
waves  become  -\-  f  Cm.,  instead  of  -1-  -J  Cm.,  at  the  cornea  of 
the  observed  eye. 

As  area  3  is  the  retina  of  the  observed  eye,  it  would  not  be 


138  DYNAMIC    FACTORS    OF   SKIASCOPV. 

proper  to  require  the  one  under  examination  to  change  his 
position,  but  the  observer  or  operator  may  approach  or  recede 
from  the  eye  under  examination,  changing  the  position  of  area 
4.  But  as  the  mirror  (area  2)  and  the  observing  eye  are  to- 
gether, any  change  of  either  requires  a  corresponding  change 
in  the  other.  That  is,  if  the  mirror  is  moved  forward  or  back, 
the  observing  eye  must  also  be  moved  in  the  same  direction 
and  the  same  distance;  and  if  the  observing  eye  is  moved  the 
mirror  must  be  moved  correspondingly.  If  the  observing  eye 
is  advanced  toward  the  observed  eye  from  a  distance  of  i  meter 
to  a  distance  of  -^-  meter,  this  afifects  the  space  in  which  the 
emergent  pencils  are  evolved.  It  may  take  the  observing  eye 
from  a  position  posterior  to  the  focal  area  to  a  position  at  it, 
or  from  a  position  at  it  to  a  position  anterior  to  it.  But  the 
advance  of  the  observing  eye  is  necessarily  accompanied  with 
advance  of  the  mirror,  and  advance  of  the  mirror  shortens  both 
intervals  i  and  2  the  same  amount.  But  as  the  evolutionary 
space  of  the  incident  waves  is  the  sum  of  intervals  i  and  2,  the 
advance  of  the  mirror  ^  meter  shortens  this  space  i  meter  by 

Fig.  37. 


taking  4  meter  from  each  interval.  This  is  shown  in  Fig.  37. 
The  change  from  a  position  i  meter  from  the  observed  eye  to 
I  meter  from  it  makes  interval  3  ^  meter,  or  -^-  what  it  was  be- 
fore, and  the  sum  of  intervals  i  and  2=1  meter,  or  ^  what  it 
was  before.  In  the  position  at  i  meter  the  incident  waves 
would  have  a  curvature  of +  |  Cm.  at  the  cornea  ot  the  observ^ed 
eye,  and  the  emergent  pencils,  if  focused  for  the  observing  eye, 
would  have  a  curvature  of  —  i  Cm.  At  ^  meter  the  incident 
pencils  at  the  cornea  of  the  observed  eye  would  be  +  i  Cm., 
while  the  emergent  pencils,  if  focused  for  the  observing  eye, 
would  be  —  2  Cm.  The  effect  of  these  changes  of  distance,  or 
length  of  the  evolutionary  spaces,  must  always  be  taken  into 
account  in  determining  the  dioptric  condition  of  the  eye  under 
examination.     Aside  from  this  consideration  of  intervals  and 


DYNAMIC   FACTORS    OF    SKIASCOPY.  1 39 

their  co-relation,  changing  the  intervals  and  the  dynamic 
effects  are  precisely  the  same  as  if  the  dioptric  power  of  the 
observed  eye  were  changed. 

4.      CORRECTING   LENSES. 

Placing  lenses  before  the  observed  eye  is  exactly  similar 
to  the  employment  of  the  accommodation  of  the  observed  eye, 
except  that  lens  changes  are  made  by  more  distinct  steps;  a 
+  2.75  D.  is  substituted  for  a  +  2.50  D.,  or  +  2.50  D.  for 
+  2.25  D.,  or  —  1.75  D.  for  —  1.50  D.  The  observer  cannot 
see  the  change  take  place,  but  he  sees  the  effect  of  the  entire 
change  resulting  from  substituting  one  lens  for  another.  But 
in  making  these  changes  of  lenses  the  operator  is  working 
always,  in  making  the  primary  correction,  toward  making  the 
area  of  reversal  coincide  with  the  fixed  plane  of  reversal  in 
his  own  eye.  His  process  is  a  process  of  gauging.  He  gets 
reverse  motion  and  brings  the  two  areas  as  close  together  as 
possible — within  .50  D.  or  .25  D.  of  each  other,  and  prescribes 
the  pOAver  between  +  " —  i  D."  In  working  out  a  case  of 
astigmatism  the  process  is  precisely  the  same,  except  that  it  is 
for  one  of  the  principal  meridians  at  a  time.  But  in  working 
out  a  case  of  astigmatism  the  static  principles  of  skiascopy  are 
relied  upon  to  a  large  extent;  that  is,  it  is  sought  to  obtain  a 
retinal  image  that  is  symmetrical  in  form,  and  it  matters  little 
whether  much  or  little  ametropia  exists  at  the  time,  so  long 
as  a  tolerably  clear  outline  of  the  luminous  area  is  displayed  at 
area  3.  A  correction  of  the  astigmatic  element  with  3  D.  of 
hypermetropia  will  correct  it  for  2  D.  of  myopia  or  for  em- 
metropia.  Astigmatism  is  really  neither  myopic  nor  hyperopic, 
nor  mixed,  nor  compound.  It  is  merely  a  difference  of  power 
in  two  chief  meridians  and  in  all  intermediate  meridians.  It 
is  the  hyperopia  or  myopia  that  is  compound,  mixed,  etc.,  not 
the  astigmatism. 

5.    MOTION  AT  LUMINOUS  AREA. 

Nothing  has  ever  been  done,  sO'  far  as  we  know,  to  make 
motion  at  the  luminous  area,  or  motion  of  the  luminous  area, 
provide  the  dynamic  factor  for  a  skiascopic  test.  Of  course, 
when   motion   is   contrary   to  the  motion   of  the   mirror,   an 


140  DYNAMIC    FACTORS    OF   SKIASCOPY. 

upward  motion  of  the  luminous  area  would  appear  as  a  down- 
ward motion,  and  a  downward  motion  as  an  upward  motion. 
Right  and  left  would  be  reversed  in  the  same  manner.  But  to 
preserve  constancy  of  motion  the  luminous  area  would  have 
to  be  made  to  vibrate  back  and  forth,  and  the  trouble  would 
be  to  keep  track  of  the  actual  motion  so  as  to  know  when  the 
apparent  motion  was  with  or  opposite  to  the  actual  motion. 
The  author  had  devised  a  very  pretty  plan  of  securing  rotary 
motion  at  the  luminous  area  under  the  impression  that  reversal 
would  cause  the  figure  to  appear  to  rotate  in  the  opposite  di- 
rection. More  careful  analysis,  however,  showed  him  that 
such  reversal  of  motion  would  not  occur.  If  the  luminous 
area  were  an  arrow  rotating  in  the  direction  of  the  hands  on  a 
dial,  inversion  of  the  figure  would  not  reverse  the  motion,  any 
more  than  inverting  a  watch  dial  would  cause  tlie  hands  to 
move  in  an  apparently  opposite  direction.  To  reverse  such 
rotary  motion  it  would  be  necessary  that  the  observer  view  the 
rotation  from  the  opposite  side  of  the  rotating  figure,  and  in- 
version in  optics  does  not  produce  this  effect.  But  reflection 
which  reverses  positions  without  inversion  produces  it.  The 
reflection  of  a  clock  face  in  a  plane  mirror  reverses  the  face 
without  inverting  it,  and  causes  the  moving  hands  to  appear 
to  be  going  in  the  opposite  direction.  It  is  difficult  to  see 
how  this  principle  could  be  applied  in  skiascopy,  although  it 
would  make  a  unique  exhibit  of  the  effects  of  reversal  if  it  could 
be  used.  Nothing  is  more  startlingly  unique,  or  anomalous, 
than  a  reversal  of  the  regular  and  natural  order  of  events.  It 
is  said  that  the  kinnetiscope  may  be  made  to  reverse  motion 
in  this  way  if  the  film  or  plate,  or  whatever  the  order  of  events 
is  recorded  upon,  is  made  to  pass  backward  through  the  ma- 
chinery. The  startling  character  of  such  an  exhibit  may  be 
appreciated  if  we  consider  its  effect  upon  the  view  of  a  dinner 
party  at  which  a  fine  roast  turkey  and  other  rich  foods  have 
been  discussed.  All  of  the  guests  will  at  once  become  en- 
gaged in  taking  food  from  their  mouths  and  putting  it  back 
upon  their  plates,  which,  in  due  time,  will  become  loaded  and 
go  back  to  mine  host,  who  will  proceed  with  it  to  build  up  on 
the  skeleton  of  a  turkey,  the  bird  as  it  came  from  the  oven- 
Half  smoked  cigars  will  spring  up  off  the  floor  to  the  hands 


DYNAMIC    FACTORS    OF   SKIASCOPY.  I4I 

and  then  to  the  mouths  of  the  smokers,  while  a  cloud  of  smoke 
will  appear  before  them  and  be  drawn  into  their  mouths.  If 
conversation  could  also  be  made  to  go  backward,  the  confusion 
of  tongues  in  the  building  of  the  tower  of  Babel  would  not  be 
a  circumstance  in  comparison. 

NEUTRALIZING  INCIDENT  PENCILS. 

We  have  referred  elsewhere  to  the  use  of  a  lens  in  a 
skiascopic  T-chimney  to  neutralize  the  pencils  of  light  from  the 
luminous  area,  or  from  a  diffusion  disc  close  to  the  flame.  The 
effect  of  the  use  of  such  a  neutralizing  lens  would  be  to  elim- 
inate inter^'als  1  and  2  as  evolutionary  spaces,  for  if  the  waves 
upon  emergence  from  such  lens  were  neutral  they  would  be 
static.  Pencils  of  light  composed  of  neutralized  waves  would 
be  precisely  the  same  as  pencils  of  light  from  infinity,  except 
for  the  element  of  aberration  contained  in  them.  If  the  ob- 
serv^ed  eye's  accommodation  were  passive  and  the  eye  were, 
either  naturally  or  artificially,  emmetropic,  the  incident  pencils 
W'Ould  give  a  clear  image  upon  the  retina,  for  there  would  be 
no  diffusion,  and  emit  neutral  pencils  to  the  observed  eye. 
This  would  provide  the  conditions  needed  to  eliminate  diffu- 
sion at  areas  3  and  4  at  the  same  time.    If  the  observed  eye  were 

Fig.  38. 


+ 


.4— Real  Luminous  <area.  5— Luminous  area  A  magnified  by  skiascopic  lens. 

C— Retinal  image,  area  3,  of  .4  or  B.     D — Anterior  image  of  0— original  of  image  at  area  4. 

ametropic  the  lens  which  corrected  its  ametropia  would,  with 
the  action  of  its  dioptric  media,  (i)  neutralize  emergent  pencils, 
and  (2)  focus  neutral  incident  pencils  at  the  retina.  The 
image  on  arec  3  would  be  clear  and  without  diffusion,  while 
the  image  of  that  image  at  area  4  would  also  be  clear  and  with- 
out diffusion,  as  shown  in  Fig.  38.     As  all  waves  in  the  evolu- 


142  DYNAMIC    FACTORS    OF    SKIASCOPi'. 

tionary  spaces  of  intervals  i,  2  and  3  would  be  neutral,  it  could 
make  no  difference  what  the  distance  of  the  mirror  from  the 
luminous  area,  of  the  observed  eye  from  the  mirror,  or  of  the 
observing  eye  from  the  observed  eye,  except  that  nearness 
would  increase  the  angle  of  vision  and  the  area  of  retinal 
images,  and  aberration  would  have  to  be  counted  with.  Were 
it  not  for  aberration  this  would  provide  the  finest  of  static  tests, 
for  the  definition  at  area  3  and  consequently  the  definition 
at  area  4  would  tell  the  whole  story.  That  lens  before  the 
observed  eye  which  gave  the  best  definition  of  some  character- 
istic figure,  as  of  a  cross,  a  square,  a  triangle,  would  be  the 
correcting  lens.  The  observer  would  be  seeing  the  luminous 
area  through  the  dioptric  media  of  the  observed  eye,  and  any 
imperfection  in  that  definition  would  be  due  to  the  observed 
eye,  which  the  lens  would  duly  correct. 

The  image  upon  area  3  is,  of  course,  very  small.  The 
luminous  figure  from  which  the  observed  eye  obtained  its" 
image  would  need  to  be  small,  because  the  lens  would  magnify 
it,  and  only  a  small  area  back  of  the  lens  would  provide  in- 
cident pencils  for  the  observed  eye.  The  amount  of  the  reduc- 
tion of  the  figure  upon  area  3  would  depend  upon  the  law  of 
images,  but  as  the  distance  of  the  retina  from  the  principal 
plane  of  the  eye  is  not  a  fixed  quantity,  and  the  use  of  a  lens  in 
front  of  the  eye  would  change  the  location  of  the  principal 
plane  of  the  combination,  it  would  be  difficult  to  obtain  the 
exact  amount.  If,  however,  the  retina  were  .8  in.  from  the 
principal  plane,  and  the  luminous  area  were  80  in.  distant, 
the  image  on  area  3  would  have  a  diameter  inversely  propor- 
tional to  these  distances,  as  compared  with  the  luminous  area. 
That  is,  the  diameter  of  the  image  would  be  to  the  diameter  of 
the  luminous  area  as  .8  is  to  80,  or  as  i  to  100,  and  be  i/ioo 
of  it.  This  image  would  be  increased  in  size  by  diffusion  when 
there  was  diffusion  at  area  3,  but  that  would  not  be  magnifica- 
tion, for  the  lens  has  its  maximum  of  magnifying  power  when 
the  object  seen  through  it  is  at  the  focus — that  is,  the  principal 
focus. 

Now,  this  image  upon  the  retina  of  the  observed  eye  is 
the  original  of  the  image  anterior  to  the  observed  eye,  if  it 
has  an  anterior  image,  which  it  will  have  if  the  observed  eye 


DYNAMIC    FACTORS    OF   SKIASCOPY.  I43 

is  myopic,  and  the  dioptric  media,  whether  with  or  without  a 
lens,  will  have  the  same  magnifying  power  upon  the  emergent 
pencils  or  anterior  image  as  it  has  upon  the  incident  pencils 
or  retinal  image  at  area  3.  Hence,  if  the  anterior  image  is 
40  in.  from  the  principal  plane  of  the  observed  eye,  the  anterior 
image  will  be  to  the  retinal  image  at  area  3  as  40  is  to  .8,  or  50 
times  as  large — that  is,  have  a  diameter  50  times  as  great  as 
that  of  the  retinal  image  at  area  3.  It  is,  then,  unnecessary  to 
make  the  distance  of  area  3  from  the  principal  plane  of  the 
•eye  an  element  or  term  in  the  proportion,  for  things  propor- 
tional to  the  same  thing  are  proportional  to  each  other,  and 
the  anterior  image  and  luminous  area  will  be  in  the  same  pro- 
portion as  their  distances  from  the  principal  plane  of  the  ob- 
served eye.  The  distance  of  the  luminous  area  is  practically 
the  sum  of  intervals  i  and  2,  while  the  distance  of  anterior 
image,  when  the  area  of  reversal  is  at  the  observing  eye,  is  the 
length  of  interval  3  or  2.  This  gives  a  rule  for  determining  the 
size  or  diameter  of  the  area  of  reversal  or  the  anterior  image. 
If  there  is  dififusion  at  area  3,  increasing  the  size  of  the  retinal 
image,  the  anterior  image  will  be  proportionately  increased 
in  size — but  that  is  dififusion  and  impairs  the  clearness  of  the 
image,  and  not  magnification. 

ELEMENT   OF  ABERRATION. 

The  element  of  aberration — aberration  produced  by  the 
chimney  lens — would  present,  perhaps,  the  greatest  difficulty 
to  overcome,  but  for  such  a  means  of  determining,  measuring 
and  correcting  ametropia  no  ordinary  expense  in  procuring  a 
lens  should  be  spared.  Many  optical  instnnnents  that  only 
reveal  certain  elements  of  ametropia  cost  $100  or  more;  an 
absolutely  reliable  lens  for  this  work  could  probably  be  made 
for  less  money,  and  it  would  provide  the  most  accurate  means 
of  determining,  measuring  and  correcting  ametropia  that  could 
be  conceived  of,  for  it  would  be  direct,  objective  and  absolutely 
accurate  for  all  forms  of  regular  ametropia.  It  would  make  the 
use  of  mydriatics  entirely  superfluous,  for  there  would  be  no 
stimulus  for  the  accommodation  to  act,  even  if  the  observing 
eye  looked  directly  into  or  at  the  mirror  or  at  the  image  of  the 
luminous  area  in  it. 


144  DYNAMIC    FACTORS    OF   SKIASCOPY. 

In  the  present  practice  of  skiascopy  the  greatest  handicaps 
are  the  accommodation  of  the  observed  eye  and  aberration 
when  the  observing  eye  approaches  the  observed  eye.  A  neu- 
tralizing actinic  lens  in  the  skiascopic  chimney  would  remove 
these  two  uncertain  and  often  annoying  features,  but  as  far  as 
the  accommodation  of  the  observed  eye  is  concerned,  that  can 
be  deposed  of  without  artificial  assistance.  The  dark  room 
and  the  mere  want  of  a  near  and  clearly  defined  object  to  fix 
the  attention  and  stimulate  the  accommodation  is  sufficient. 
The  ciliary  may  not  be  as  fully  relaxed  as  with  the  use  of  the 
drug,  but  corrections  made  under  the  action  of  the  drug  are 
mere  guesswork,  for  usually  something  is  subtracted  from  the 
entire  amount  of  revealed  error,  and  the  object  of  using  the 
drug  is  thus  discredited  and  discounted  in  advance.  If  not 
used  at  all,  it  will  not  be  necessary  to  discount  your  own 
diagnosis,  which  is  not  an  act  to  inspire  confidence  in  yourself. 
It  is. practically  saying  that  the  use  of  the  drug  gives  lying- 
results,  and  therefore  you  must  discount  its  revelations  on 
account  of  their  unreliability.  It  would  be  better  to  repudiate 
the  liar  wholly  and  endeavor  to  ascertain  the  amount  of  ame- 
tropia by  more  reliable  means. 

The  accommodation  of  the  observing  eye  is,  of  course,, 
allowed  full  play  in  a  skiascopic  examination — that  is,  when  it 
can  gain  anything  by  it.  But  during  the  critical  periods  of 
such  examination  the  accommodation  of  the  observing  eye 
might  as  well  be  non-existing,  for  it  can  accomplish  nothing 
either  when  relaxed  or  active.  The  eye  receives  a  class  of 
pencils  of  light  it  was  never  designed  to  find  in  nature.  It  is 
wholly  incompetent  to  produce  visual  effects  with  those  pecu- 
liar pencils  or  waves.  That  it  does  secure  certain  visual  effects 
is  due  to  its  adaptation  to  circumstances  that  enable  it  to  get 
results  though  not  really  visual  ones  in  spite  of  seemingly 
insurmountable  obstacles.  It  matters  little  what  the  accom- 
modation of  the  observing  eye  is  or  may  be.  It  is  not  a  factor 
in  the  conclusions  to  be  drawn,  whether  it  be  used  or  unused. 

THE   QUESTION   OF   DISTANCE. 

The  nearer  the  observing  eye  is  to  the  observed  eye,  the 
larger  the  image  at  area  4  of  the  pupil  of  the  observed  eye.  But 


DYNAMIC    FACTORS    OF    SKIASCOPY.  I45 

approach  of  the  observing  to  the  observed  eye,  when  the 
area  of  reversal  is  brought,  by  a  lens,  to  the  fixed  plane  of 
reversal,  the  greater  is  the  degree  of  aberration.  Positive  aber- 
ration gives  the  marginal  areas  of  the  dioptric  media — ^those 
areas  near  the  margin  of  the  pupil — a  shorter  focal  length. 
That  is,  the  peripheral  areas  of  the  transmitted  waves  come  to 
centers  of  curvature  or  foci  nearer  the  eye  than  the  central 
areas.  If  the  observing  eye  is  at  the  focal  distance  for  the 
central  areas  of  the  lens  back  of  the  pupil,  and  of  the  cornea  in 
front  of  it,  it  is  just  beyond  the  focal  point  for  peripheral  areas. 
In  that  case  the  central  area  of  the  pupil  has  the  appearances 
characteristic  in  this  location — it  shows  no  image  or  light.  But 
the  margin  of  the  "pupil,  which  focuses  the  peripheral  areas  of 
the  waves  anterior  to  the  observing  eye,  shows  light  and  mo- 
tion. If  the  observing  eye  is  advanced  toward  the  observed 
eye  it  comes  to  the  focal  point  of  the  peripheral  areas  of  the 
waves,  and  light  and  motion  disappear  at  the  margin,  but 
appear  at  the  center  of  the  pupil.  But  between  these  two  ex- 
treme positions  every  area  of  the  pupil  shows  alternately  light 
and  motion  and  shadow  and  absence  of  motion,  for  the  differ- 
ent areas  of  the  waves  do  not  focus  at  two  different  points 
merely,  but  along  a  line  connecting  the  two.  With  the  ad- 
vance of  the  eye  from  the  farther  to  Hie  nearer  point  light  and 
dark  areas  advance  inward  toward  the  center  of  the  pupil. 
With  its  recession  from  the  near  to  the  farther  point  they  de- 
velop at  the  center  and  advance  toward  the  margin  of  the  pupil. 
The  area  of  darkness  is  the  area  whose  focus  is  at  the  plane  of 
reversal  in  the  observing  eye.  Hence,  when  there  is  a  central 
and  marginal  area  of  light,  with  a  dark  ring  between  them,  in 
positive  aberration  the  central  area  of  light  will  show  motion 
with  the  mirror  and  the  marginal  area  motion  against  it.  Tliis 
is  perceptible  in  the  most  regular  cases  of  natural  or  artificial 
ametropia.  But  if  the  central  area  shows  motion  against  the 
mirror,  while  the  margin  shows  motion  with  it,  negative  aber- 
ration, or  higher  power  for  the  central  areas  of  the  dioptric 
body,  are  shown. 

But  these  appearances,  due  to  aberration,  manifest  them- 
selves really  at  area  4,  which  projects  them  into  the  pupil  of  the 
observed  eye.    They  are  concentric  rings  or  a  central  area  of 


146  DYNAMIC   FACTORS    OF   SKIASCOPY. 

diffusion  at  area  4.  Aberration  is  but  a  special  form  of  diffu- 
sion— diffusion  due  to  the  inaccurate  focusing  of  each  indi- 
vidual wave.  If  one  area  focuses  at  the  fixed  plane  of  reversal, 
another  area  focuses  forward  or  back  of  it,  producing  diffusion 
at  the  retina.  It  is  possible  to  obtain  the  degree  and  kind  of 
aberration  by  noting  the  distance  from  central  and  marginal 
diffusion  positions  to  central  and  marginal  darkness  or  shadow. 
The  three  areas  of  aberration — central,  subcentral  and  mar- 
ginal— cannot  usually  be  seen  at  one  meter,  but  are  clearly  dis- 
cernible at  I  meter  or  less.  At  one  meter,  or  beyond  it,  two  of 
the  areas  only — the  central  and  subcentral,  the  latter  having 
become  marginal — can  be  seen.  At  two  meters  even  the 
second  or  subcentral  area  is  difficult  to  see,  but  distance  makes 
the  observed  pupil  so  small  that  it  is  difficult  to  distinguish 
different  areas  of  it. 

The  advantages  of  a  long  working  distance — two  meters 
or  more — are  due  to  the  long  evolutionary  space  of  the  incident 
pencils.  Such  advantage  may  be  obtained  at  a  working  dis- 
tance of  one  meter,  by  using  a  large  light,  about  the  size  of  a 
Chinese  lantern  or  porcelain  globe,  placed  four  meters  back 
of  the  patient  while  the  observer  is  one  meter  in  front  of  him. 
A  large  skiascopic  mirror  should  then  be  used,  and  the  patient 
should  be  directed  to  look  at  (and  accommodate  for)  the  vir- 
tual image  in  the  mirror.  Only  ^  D.  of  the  accommodation 
will  be  involved,  and  when  the  eye  is  made  i  D.  myopic  by 
the  trial  case  lens,  the  pupillary  display  shows  reversal  very 
distinctly  close  to  the  point  of  reversal. 

As  to  the  zonular  appearances  for  a  near  working  dis- 
tance, the  teaching  that  the  central  area  of  the  pupil  is  of 
special  importance  because  it  refracts  for  the  macular  region 
specially  is  wrong.  Whether  foci  fall  upon  the  macular 
region  or  not  depends  upon  the  nearness  of  the  points  in  the 
object  to  the  visual  axis,  and  each  pencil  from  the  object, 
whether  near  such  axis  or  not,  is  refracted  by  the  entire  pupil- 
lary area.  There  is  no  extra  visual  area  to  the  pupil,  and  the 
central,  subcentral  and  peripheral  areas  refract  one  pencil  as 
much  as  another.  The  oblique  pencils  are  refracted  by  the 
central,  as  well  as  peripheral  areas  of  the  pupil,  the  pencils 
near  the  visual  axis  are  refracted  by  the  peripheral  as  well  as 


DYNAMIC  FACTORS  OF  SKIASCOPY.  I47 

the  central  areas.  The  zonular  appearance  is  a  subjective 
phenomena,  displayed  at  area  4  only.  In  skiascopy  only  mac- 
ular areas  are  concerned.  There  is  no  display  not  on  the 
macula. 

STIMULUS    OF    ACCOMMODATION. 

In  skiascopy,  as  practiced,  there  is  always  diffusion  at  area 
3  or  area  4,  and  usually  at  both,  at  the  critical  point  of  the 
examination — when  the  area  of  reversal  is  at  the  fixed  plane 
of  reversal  of  the  observing  eye.  At  area  3  there  is  no  stimulus 
for  the  accommodation  to  act,  for  the  observed  eye  is  not 
directed  to  the  mirror,  and  the  image  does  not  center  at  the 
macula.  At  area  4  there  is  stimulus  for  the  observing  eye,  but 
its  power  of  accommodation  is  entirely  inadequate  to  over- 
come the  diffusion,  except  for  hyperopia  and  emmetropia,  and 
then  it  cannot,  of  course,  overcome  the  diffusion  at  area  3, 
from  which  the  pencils  by  which  it  obtains  its  image  come. 

What  stimulates  the  accommodation  and  causes  the  ciliary 
to  act?  Undoubtedly  the  stimulus  is  twofold  in  character. 
The  double  stimulus  is  (i)  diffusion  at  the  retina  and  an  im- 
perfect image,  and  (2)  the  want  of  correspondence  of  the  retinal 
images  in  the  two  eyes  or  on  the  two  retinae.  In  skiascopy  the 
binocular  principle  has  little  opportynity  to  act,  and  the  stim- 
ulus is  principally  diffusion.  The  observing  eye  probably 
searches  for  a  better  retinal  image  than  it  is  able  to  obtain,  but 
its  failure  to  eliminate  diffusion  must  cause  the  accommodation 
to  relax  after  a  vain  attempt.  Even  when  the  observing  eye, 
with  relaxed  accommodation,  is  unable  to  focus  the  emergent 
pencils  at  the  retina,  as  in  emmetropia  of  the  observed  eye,  or 
when,  with  accommodation,  it  is  able  to  focus  the  pencils,  as  in 
hyperopia,  diffusion  at  area  3  is  a  confusing  feature  and  tends 
to  quiet  the  accommodation  because  of  the  impossibility  of 
obtaining  a  sharp  definition  of  the  reflex  or  image  at  area  3. 
10 


CHAPTER  VII. 


THE    STUDY    OF    THE    EYE    BY    SKIASCOPY.       EMMETROPIA    AND 

SYMMETRICAL    AMETROPIA.       THE    THREE    PRIMARY 

CASES.      STATIC  AND  DYNAMIC  APPEARANCES. 


THE  practical  field  of  the  skiascopist  is  confined  to  one 
small  objective  space  or  area — the  pupil  of  the  observed 
eye.  In  that  field  appears,  under  different  skiascopic  con- 
ditions, a  full  and  complete  display,  answering  all  the  ques- 
tions that  may  be  propounded  relative  to  the  observed  eye's 
dioptric  condition.  The  skiascopist  has  but  to  provide  the 
conditions  and  read  the  result  in  the  objective  pupil.  But  all 
so-called  visual  objective  appearances  are  the  projection  of  a 
subjective  retinal  display.  Skiascopy  is  no  exception  to  this 
rule.  It  is  really  a  special  example  of  it,  for  some  of  the  ap- 
pearances in  skiascopy  are  entirely  subjective,  having  no  ob- 
jective phenomena  to  account  for  them.  That  the  observer 
projects  such  phenomena  makes  them  none  the  less  subjective 
in  fact. 

The  first  essential  of  correct  skiascopic  work  is  a  normal 
subjective  retina,  a  retina  sensitive  to  light.  It  need  not  be 
emmetropic,  although  emmetropia  is  an  advantage,  for  the 
most  emmetropic  eye  could  do  practically  nothing  with  pencils 
of  light  anteriorly  focused  at  its  pupil  or  cornea,  and  an  ame- 
tropic  eye  could  not  be  more  incompetent,  whether  its  error 
were  symmetrical  or  otherwise.  We  call  the  test  objective; 
yet,  in  another  sense,  it  is  subjective,  being  made  objective  by 
projection  merely,  as  is  the  case  in  all  visual  objectivity.  The 
skiascopist  is  not  required  to  take  the  evidence  of  his  patient  to 
determine  the  kind  and  degree  of  ametropia  revealed  in  the 
skiascopic  examination.  His  own  retina  displays  all  the  data 
necessary. 

The  movement  of  the  reflex  across  the  pupil  or  the  motion 

148 


THE   STUDY   OF  THE   EYE   BY   SKIASCOPY.  149 

of  the  image  at  area  3  is,  when  a  plane  mirror  is  used,  always 
in  one  direction,  whether  the  eye  be  hyperopia,  emmetropic  or 
myopic — that  is,  with  the  mirror  or  light  on  the  face.  But 
the  subjective  motion,  or  motion  at  area  4,  may  be  the  same  as 
motion  at  area  3,  or  opposite  from  it,  on  account  of  optical 
modification  of  the  emergent  pencils  by  the  observed  eye. 
When  the  two  motions  correspond — both  being  to  the  right 
or  both  to  the  left — the  observer  projects  such  motion  as  mo- 
tion opposite  to  motion  at  area  3.  But  when  the  two  motions 
are  opposite — one  being  to  the  right,  the  other  to  the  left — the 
observer  projects  such  motion  as  motion  with  motion  at  area  3. 
In  other  words,  the  motions  at  the  two  areas  to  correspond 
must  be  really  opposite,  while  to  be  opposite  or  appear  oppo- 
site they  must  correspond. 

Motion  at  area  3,  with  a  plane  mirror,  is  always  the  same: 
with  the  mirror  or  light  on  the  face;  but  motion  at  area  4  is 
not,  therefore,  the  opposite,  nor  the  same.  It  may  be  one  or 
the  other  or  neither.  What  it  is  depends  upon  the  dioptric 
media  of  the  observed  eye.  It  is  because  the  direction  of  mo- 
tion at  area  4  depends  upon  the  dioptric  condition  of  the 
observed  eye  that  we  are  able,  by  comparing  motions,  to  deter- 
mine and  measure  the  dioptric  condition  of  the  observed  eye. 

The  appearances  of  emmetropia  'and  symmetrical  ame- 
tropia present  the  same  features,  for  it  is  only  necessary  to 
place  a  spherical  lens  before  the  emmetropic  eye  to  make  it, 
artificially,  symmetrically  ametropia — ametropia  to  the  same 
extent  and  of  the  same  kind  in  all  meridians;  and  it  is  only 
necessary  to  place  a  correcting  spherical  lens  before  a  sym- 
metrically ametropia  eye  to  make  it  artificially  emmetropia. 
Either  condition  is,  with  a  spherical  lens  of  the  right  kind  and 
power,  reducible  to  the  other.  But  hyperopia  may  not  only 
be  reduced  to  emmetropia,  but  to  myopia,  by  the  same  means; 
and  myopia  may,  in  like  manner,  be  reduced  to  hyperopia.  An 
emmetropic  eye  with  a  +  2  D.  sph.  lens  before  it  becomes,  arti- 
ficially, 2  diopters  myopic.  With  a  —  2D.  sph.  lens  before  it, 
it  becomes  2  diopters  hyperopia.  But  an  eye  that  is  2  diopters 
hyperopia  becomes,  with  a  +  2  D.  sph.  lens  before  it,  artificially 
emmetropic.  With  a  +  3  D.  sph.  lens  before  it  it  becomes, 
artificially,  i  diopter  myopic.     In  the  same  manner  a  —  2D, 


150  THE   STUDY   OF  THE   EYE   BY   SKIASCOPY. 

sph.  lens  reduces  an  eye  2  diopters  myopic  to  emmetropia,  and 
a  —  3D.  sph.  lens  makes  it  i  diopter  hyperopic.  The  study  of 
emmetropia,  myopia  and  hyperopia  by  skiascopy  is,  then,  prac- 
tically the  same,  or  exactly  the  same,  except  that  you  have  a 
different  condition  of  refraction  to  start  with.  In  the  practical 
work,  then,  of  making-  a  skiascopic  examination  of  an  eye,  it 
matters  little  whether,  to  start  with,  it  is  myopic  or  hyperopic, 
for  the  initial  dioptric  condition  can  only  afifect  the  direction 
of  the  primary  work — that  of  bringing  area  of  reversal,  focal 
area  or  image  anterior  to  the  observed  eye,  to  the  fixed  plane 
of  reversal  in  the  observing  eye.  The  analysis  of  one  case  is 
practically  the  analysis  of  all  cases  of  symmetrical  ametropia. 
We  will,  then,  consider  the  steps  in  a  skiascopic  examination, 
with  these  facts  in  view. 

I.      THE   INITIAL   CONDITION. 

The  first  step,  then,  is  to  determine  the  initial  condition — 
not  necessarily  the  absolute  condition,  although  it  would  be 
better  to  do  so — but  the  relative  condition — whether  the  focal 
area  or  image  within  the  observing  eye  is  posterior  or  anterior 
or  at  the  fixed  plane  of  reversal;  or  whether  the  external  po- 
tential image  (if  there  is  one  anterior  to  the  observed  eye)  is 
posterior  or  anterior  or  at  the  cornea  of  the  observing  eye. 
This  will  be  at  once  revealed  by  a  glance  through  the  perfora- 
tion in  the  mirror  when  the  area  of  light  on  the  face  is  made 
to  pass  across  the  observed  eye,  for  one  of  three  effects  will  be 
produced: 

Case  I.  The  red  reflex  will  appear  and  move  across  the 
pupil  with  the  light  on  the  face  or  in  the  same  direction  as  the 
mirror  is  tilted,  or 

Case  11.  A  large  reflex,  covering  the  entire  area  of  the 
pupil,  will  appear  instantaneously  and  disappear  as  quickly, 
so  quickly  that  its  direction  is  indeterminate,  or 

Case  III.  A  clearly  marked  reflex  will  appear  and  move 
across  the  pupil  opposite  to  motion  of  the  light  on  the  face 
or  the  motion  of  the  mirror. 


THE   STUDY    OF   THE   EYE    BY   SKIASCOPY,  I5I 

The  above  are  the  essential  characteristics  at  a  point  of 
observation  one  meter  from  the  observed  eye.  Each,  however, 
has  its  special  features  that  need  to  be  more  particularly  dwelt 
upon.  We  have  said,  also,  that  these  appearances  do  not  reveal 
the  absolute  condition — that  is,  whether  the  eye  is  hyperopic, 
emmetropic  or  myopic — and  that  it  would  be  better  to  deter- 
mine that  at  once,  which  may  be  done  by  a  method  to  be 
described  later.  In  considering  the  special  features  of  each 
case  we  shall  take  the  first  and  third  first,  and  consider  the 
second,  which  is  the  most  important,  last.  Although  these 
appearances  are  characteristic  of  observations  from  one  meter, 
study  from  a  nearer  point  is  not  essentially  different,  except 
that  the  effects  of  aberration  are  more  pronounced.  This 
merely  reduces  the  area  to  be  studied  specially  from  the  whole 
pupil  to  a  central  area  of  the  pupil — the  "visual"  area,  as  Dr. 
Jackson  calls  it.  The  appearances  described  are  objective — 
displayed  in  an  objective  pupil — and  yet  both  the  display  and 
the  pupil  in  which  the  display  appears  are  imaged  on  area  4 — 
the  subjective  area.  There  are^  moreover,  effects  at  area  4  that 
do  not  occur  at  area  3  at  all,  but  are  the  results  of  optical  mod- 
ification of  the  pencils  on  their  way  from  area  3  to  area  4,  but 
which  the  observer  projects  into  the  pupil  of  the  observed  eye, 
as  though  the  phenomena  occurred  there.  Reversal  of  mo- 
tion is  a  phenomenon  of  this  kind.  There  is  no  foundation  for 
it  at  area  3.  It  is  the  product  of  optical  modification  of  the 
emitted  pencils  entirely. 

CASE    I. 

Three  conditions  may  produce  the  effects  noted  in  case  i : 
(i)  Hyperopia,  (2)  emmetropia,  (3)  myopia  of  less  than  one 
diopter.  Motion  with  the  mirror  does  not,  then,  show  in  this 
case  the  absolute  condition.  But  there  will  be  a  marked  differ- 
ence in  the  appearances  in  the  three  different  conditions,  not- 
withstanding the  fact  that  motion  will  be  the  same  in  all.  In 
hyperopia  motion  is  sluggish,  but  it  is  more  sluggish  in  high 
than  in  low  degrees  of  hyperopia.  In  emmetropia  motion  will 
not  be  rapid,  but  it  will  be  more  rapid  than  in  hyperopia.  In 
myopia  motion  will  be  more  rapid,  especially  if  the  myopia 


152  THE   STUDY   OF  THE   EYE   BY   SKIASCOPY. 

amounts  to  nearly  one  diopter,  for  with  one  diopter  of  myopia 
we  have  case  2.  In  high  degrees  of  hyperopia  the  extent  of 
diffusion  at  area  3  is  large,  which  makes  the  real  reflex  large; 
but  magnification  is  not  at  its  highest,  since  the  emitted  pencils 
are  not  neutralized,  which  makes  it  appear  small,  and  the 
illumination  is  weak.  The  minor  pencils  that  reach  the  observ- 
ing eye  are  small,  but  focused  at  area  4.  In  emmetropia  of  the 
observed  eye  there  is  less  dififusion  at  area  3  and  a  brighter 
reflex.  The  emergent  pencils,  which  will  be  neutralized  at  the 
cornea  of  the  observed  eye,  will  also  be  more  intense,  or  pro- 
vide larger  minor  pencils — pencils  that  embrace  more  action, 
because  they  are  a  larger  part  of  the  major  emergent  pencils. 
Motion  at  area  3  is  more  rapid  because  the  potential  image  is 
nearer  the  retina,  although  still  posterior  to  it. 

But  passing  the  emmetropic  and  entering  the  myopic 
field — myopia  of  the  observed  eye — we  arrive  at  more  powerful 
skiascopic  phenomena.  The  image  of  the  luminous  area  ap- 
proaches sharp  definition  at  area  3.  If  the  eye  is,  say  f  D. 
myopic,  and  the  luminous  area  is,  by  way  of  the  mirror,  i^ 
■meters  from  the  observed  eye,  all  the  incident  pencils  of  light 
from  the  luminous  area  will  focus  at  area  3,  producing  a  sharp 
•clear  image.  This  will  bring  the  incident  and  emergent  pencils 
together,  point  to  point.  The  same  dioptric  media  that  focuses 
the  incident  pencils  at  the  retina  will  focus  the  emergent  pencils 
i^  meters  anterior  to  the  retina.  Hence,  when  the  waves  of 
these  pencils,  on  their  way  to  their  potential  foci,  ^  meter  back 
of  the  observing  eye,  reach  its  cornea,  they  will  have  a  curv- 
ature of  —  3  Cm.  The  dioptric  media  of  the  observing  eye  will 
focus  these  pencils,  but  not  at  the  retina.  It  will  focus  them 
far  forward  of  the  retina  and  well  toward  the  fixed  plane  of 
reversal,  but  not  at  it.  The  result  is  dififusion  at  area  4,  though 
dififusion  will  be  confined  within  the  imaged  pupil  of  the  ob- 
served eye  on  area  4.  Motion  will  be  quite  rapid,  and  the  red 
reflex  will  be  brilliant,  though  large.  It  will  be  large  because 
of  dififusion,  and  brilliant  because  of  the  intensity  of  the  pencils 
which  are  drawing  near  their  potential  foci  when  admitted  into 
the  observing  eye.  Dififusion  and  the  intensity  of  these  pencils 
increase  together,  for  dififusion  augments  until  the  focal  area 
reaches  the  fixed  plane  of  reversal  at  the  pupil.    The  intensity 


THE  STUDY   OF  THE   EYE   BY   SKIASCOPY.  1 53 

of  each  pencil  is  also  greatest  there,  for  it  then  pours  its  full 
force  into  the  eye. 

This  efifect  is  observable  when  the  eye  looks  at  the  reflec- 
tion of  a  luminous  area,  as  of  the  flame  of  a  lamp,  in  a  concave 
mirror,  from  a  position  near  the  focal  area  of  the  flame;  or  at 
a  flame  through  a  lens  from  the  focus  of  the  lens  conjugate  to 
a  flame.  Of  course  the  pencils  are  more  intense  than  those 
emitted  usually  by  an  eye  through  its  dioptric  media  from  an 
image  on  the  retina.  But  except  for  the  source  of  light  being 
an  image  of  a  light,  instead  of  a  light,  the  two  cases  are  exactly 
similar.  The  dioptric  media  that  produces  the  retinal  image  at 
area  3  is  the  same  that  focuses  the  emergent  pencils.  So  that 
in  myopia  of  less  than  one  diopter  the  red  reflex  is  not  only 
apparently  increased  in  size,  but  it  loses  none  of  its  brilliancy 
by  diffusion  because  of  the  greater  intensity  of  the  pencils,  or 
greater  volume  of  light.  In  hyperopia  of  the  observed  eye  the 
emitted  pencils  are  focused  by  the  use  of  the  accommodation 
of  the  observing  eye;  in  emmetropia  no  accommodation  is  re- 
quired. In  slight  myopia  the  observing  eye  has  no  means  of 
focusing  the  emitted  pencils  upon  the  retina.  Its  static  refrac- 
tion focuses  them  forward  of  the  retina,  and  its  dynamic  powers 
do  not  aid  it  in  the  least. 

Figs.  39  and  40  illustrate  case'i.  The  light  in  the  pupil 
is  disappearing  behind  the  iris  in  the  same  direction  that  the 
area  of  light  is  passing  off  the  observed  eye — both  being  to  the 
left  or  both  to  the  right;  or  the  light  may  be  considered  as 
entering  the  pupil  from  the  same  direction  as  the  area  of  light 
on  the  face  is  passing  over  the  observed  eye.  The  reflex 
shows  the  same  arc  of  a  circle  as  the  arc  of  the  luminous  area 
to  which  it  corresponds.  It  doesn't  correspond  to  the  light  on 
the  face,  which  takes  its  shape  from  the  mirror,  but  is  a  true 
image  of  the  luminous  area.  The  extent  of  the  reflex  or  image 
at  area  3  varies  considerably.  Its  extent  depends  upon  (i)  the 
extent  of  the  luminous  area,  and  (2)  the  amount  of  diffusion  at 
area  3,  due  partly  to  the  eye's  emmetropia  and  partly  to  its 
being  out  of  focus  for  the  light.  But  the  apparent  extent  of 
the  red  reflex,  as  well  as  its  apparent  motion,  depends  also,  and 
chiefly,  upon  the  effects  at  area  4,  for  diffusion  at  area  3  may 
be  slight  or  nothing,  while  at  area  4  the  maximum,  or  nearly 


154 


THE  STUDY  OF  THE  EYE  BY  SKIASCOPY. 


the  maxiniiim,  of  diffusion  prevails.  The  display  of  diffusion 
at  area  4  is  limited  to  the  image  of  the  objective  pupil  on  that 
area,  however.  The  image  on  area  3  behind  the  iris  of  the 
observed  eye  is  not  shown,  but  only  that  area  that  the  iris  does 
not  conceal.  The  apparent  extent  of  the  reflex  grows  until  the 
focal  area  reaches  the  fixed  plane  of  reversal  of  the  observing 
eye,  as  shown  by  the  arc  separating  the  reflex  from  the  dark 


Fig.  39. 


areas,  although  the  principal  part  of  it  may  be  concealed.  The 
display  in  the  pupil  is  quite  a  different  optical  quantity  than 
the  iris  surrounding  the  pupil.  The  latter  is  back  of  the  cornea 
merely  while  the  reflex  is  back  of  the  cornea  and  lens. 

Figs.  41  and  42  represent  displays  in  the  pupil  under  dif- 
ferent optical  conditions.  Fig.  41  shows  a  small  luminous  area 
with  little  diffusion  at  area  3,  and  none  at  area  4  except  the 
copy  of  that  at  area  3,  for  the  observed  eye  is  emmetropic,  or 
but  slightly  hyperopic.  Fig.  42  may  represent  the  same  lumin- 
ous area  as  Fig.  41,  but  with  little  or  no  diffusion  at 
area  3  but  nearly  the  maximum  of  diffusion  at  area  4.  It 
shows  that  the  point  of  reversal  is  nearly  reached,  and  that 
motion  is  very  rapid.    The  eye  in  Fig.  42  is  myopic,  but  if  mo 


Fig.  41.     Page  154. 


Fig.  42.     Page  154. 


Fig.  40.     Page  158. 


Fig.  47.     Page  15S. 


THE   STUDY   OF  THE   EYE   BY    SKIASCOPY.  1 55 

tion  is  still  with  the  mirror,  it  is  less  than  one  diopter,  although 
near  that  amount. 

CASE  3. 

In  case  3,  motion  is  against  the  mirror  and  light  on  the 
face.  There  is  an  actual  image  between  the  observed  and 
observing  eye — an  aerial  image,  so-called.  All  the  emitted 
pencils  are  individually  transposed  and  collectively  inverted  at 
this  aerial  image,  or  focal  area  anterior  to  the  observed  eye, 
and  from  such  image  or  area  the  pencils  that  reach  the  observ- 
ing eye  are  evolved.  It  is,  to  the  observing  eye,  as  though  the 
red  reflex  were  at  this  area,  instead  of  being  at  the  retina  of 
the  observed  eye,  although  projection  places  it  in  the  pupil 
of  the  observed  eye — the  nearest  reacting  surface  in  the  line  of 
vision.  The  observing  eye  re-focuses  these  pencils  upon  its 
retina  as  nearly  as  may  be.  Its  ability  to  refocus  the  pencils 
depends  upon  the  nearness  of  the  aerial  image.  If  it  is  within 
its  punctum  proximum  it  will  be  unable  to  re-focus  them  at  the 
retina,  and  diffusion  will  prevail  at  area  4.  But  if  the  aerial 
image  is  beyond  the  observing  eye's  punctum  proximum,  it 
will  be  able  to  re-focus  them.  In  either  case  there  will  be  an 
image,  or  the  semblance  of  an  image,  at  area  4,  the  inverse  ot 
the  aerial  image,  and  therefore  the  same  in  position  as  the 
image  at  area  3.  But  motion  will  appear  to  be  opposite  to  the 
mirror  in  the  objective  pupil,  for  this  anterior  aerial  image  will 
move  oppositely,  causing  the  image  at  area  4  to  move  in  the 
same  direction  as  the  reflex  in  the  observed  eye.  The  ob- 
server, hoAvever,  projects  this  motion  as  motion  opposite  to 
real  motion  of  the  reflex. 

Case  3  shows  positively  myopia  of  more  than  one  diopter, 
when  the  working  distance  is  one  meter.  But  case  i  does  not 
show  absolutely  that  the  observed  eye  is  hyperopic,  myopic  or 
emmetropic.  Rapidity  of  motion  is,  however,  a  pretty  good 
indication  of  the  condition  of  the  observed  eye.  The  degree 
of  myopia  above  one  diopter  is  also  quite  clearly  shown  by  the 
rapidity  of  motion  and  extent  of  the  reflex  in  case  3.  The 
nearer  the  aerial  image  is  to  the  observing  eye  the  more  rapid 
the  motion.  The  motions  of  these  images  and  the  intervals 
between  them  is  a  good  deal  like  the  play  of  the  arms  of  a  sys- 
tem of  compound  levers,  in  which  the  optical  centers  of  the 


156  THE   STUDY   OF  THE   EYE   BY   SKIASCOPY. 

dioptric  media  of  the  observed  and  observing  eye  are  the  ful- 
crums  and  the  distances  from  the  hght  to  the  fulcrum,  and 
from  the  fulcrum  to  the  retina  are  respectively  the  long  and 
short  arms  of  the  levers,  the  image  at  the  retina  of  the  observed 
eye,  or  at  the  potential  focus,  corresponding  to  the  weight. 
But  this  weight  becomes  the  power  in  the  emergent  pencils,  the 
new  weight  being  the  anterior  image,  and  the  fulcrum  the 
optical  center  of  the  observed  eye.  But  the  anterior  image  be- 
comes in  turn  the  power  for  a  new  lever  whose  fulcrum  is  the 
optical  center  of  the  observing  eye,  the  power-arm  reaching 
from  the  anterior  image  to  such  center  or  fulcrum,  and  the 
weight-arm  reaching  from  the  fulcrum  to  the  retina,  or  to  the 


Fig.  43. 


potential  image  back  of  the  retina,  sr.  Fig.  43  illustrates  such 
a  system  of  compound  levers,  B,  the  dioptric  media  of  the 
observed  eye,  being  the  fulcrum  for  the  incident  pencils  from 
A,  the  luminous  area.  A  B  is  the  power-arm  of  the  lever,  and 
B  D  is  the  weight-arm,  D  being  the  location  of  the  potential 
image  back  of  m  n,  or  area  3.  But  it  is  at  C  that  the  power  is 
applied,  or  rather  that  the  work  is  done.  It  takes  quite  a 
movement  at  A  to  produce  a  slight  movement  at  C.  Move- 
ment at  A  is  produced  by  tilting  the  mirror.  But  a  slight 
movement  at  C  produces  a  considerable  movement  at  F,  on 
account  of  the  length  of  the  arm  B  F  as  compared  with  the 
length  of  C  B.  But  as  F  is  very  near  G,  the  dioptric  media  of 
the  observing  eye,  or  fulcrum  of  the  lever  F  T,  a  slight  move- 
ment of  F  produces  a  greater  movement  at  T,  or  even  at  H 
which  is  much  nearer  G.  In  this  case  T  represents  the  potential 
image  of  the  refocused  pencils,  while  H  represents  the  diffuse 
image  on  area  4.  The  nearer  F  is  to  G  the  greater  the  motion 
at  H  with  the  least  motion  of  F.  The  nearer  the  focal  area  to 
the  cornea  of  the  observing  eye,  the  more  rapid  the  motion  a' 


THE   STUDY   OF  THE   EYE   BY   SKIASCOPY. 


157 


area  4,  whatever  the  results  at  area  3.     Motion  may  be  very 
sHght  at  area  3,  but  too  swift  to  be  seen  at  area  4. 

Figs.  44  and  45  represent  motion  against  the  mirror,  or 
light  on  the  face.  The  reflex  in  the  pupil  is  seen  disappear- 
ing behind  the  iris  in  the  opposite  direction  from  that  in 
which  the  light  on  the  face  is  passing  off  the  observed  eye;  or 


^< 

jO^ 

y 

JJm 

J 

<4>^    ^"""^fcin. 

i 

^^B 

Fig.  44. 


Fig.  45. 


we  may  regard  the  light  or  reflex  as  entering  the  pupil  from 
the  opposite  direction  to  that  in  which  the  light  on  the  face 
is  passing  over  the  eye.  The  size  of  the  reflex  varies  in  case  3 
the  same  as  in  case  2,  and  depends  on  precisely  the  same  princi- 
ples. We  may  readily  determine  the  exact  size  of  the  aerial  im- 
age in  case  3  by  the  law  of  images,  but  diffusion  at  area  3  in- 
creases its  size  somewhat.  But  it  is  not  the  size  alone  of  this 
image  that  determines  the  size  of  the  reflex,  but  its  nearness  to 
the  observing  eye.  or  to  its  fixed  plane  of  reversal.  It  is  then 
that  diffusion  at  area  4  reaches  the  maximum,  or  becomes  in- 
definite, and  the  case  becomes  case  2. 

CASE  2. 
This  is  the  condition  toward  which  we  begin  to  work  in 
case  I  or  case  3.    The  object — the  primary  object — is  to  reduce 


158  THE   STUDY   OF  THE   EYE   BY   SKIASCOPY. 

the  initial  condition,  whatever  it  may  be,  to  case  2 — to  develop 
the  maximum  of  diffusion  at  area  4,  and  eliminate  motion  in 
the  objective  pupil.  Motion  is  eliminated  because,  of  all  the 
pencils  that  enter  the  pupil  of  the  observing  eye,  none  are  indi- 
vidualized upon  the  retina.  Each  spreads  over  the  same  area 
as  the  others,  producing  light  at  area  4  merely,  but  no  image. 
Motion  is  really  most  rapid  at  the  culmination  of  diffusion,  but 
as  the  pencils  are  not  individualized  we  cannot  distinguish  one 
from  the  other.  In  case  2  we  get  a  kaleidoscopic  view  of  the 
refiex.  It  appears  as  a  brilliant  glow  in  the  objective  pupil, 
but  the  glow  vanishes  at  a  touch,  as  though  the  light  had  been 
extinguished  by  a  breath  of  air,  not  moved  away.  We  judge 
the  result  usually  by  gauging — that  is,  by  taking  a  position  or 
using  a  correction  midway  between  motion  with  and  motion 
against  the  mirror.  At  one  meter  the  whole  pupil  is  usually 
homogeneous — either  filled  with  light  or  darkness  at  reversal. 
The  same  is  true  for  distances  greater  than  one  meter.  But 
at  nearer  points  than  one  meter  we  develop  the  zonular  ap- 
pearances due  to  aberration.  In  that  case  the  central  area  of 
the  pupil — the  "visual''  area  as  Dr.  Jackson  terms  it — may  be 
the  neutral  area,  or  the  periphery  of  the  pupil  may  be  neutral- 
ized while  the  central  area  shows  motion.  But  the  neutral 
zone  may  not  be  central  or  peripheral,  but  sub-central,  and  ap- 
pear as  a  darker  ring  around  an  unneutralized  central  area  of 
light,  while  the  periphery  is  fringed  also  by  an  unneutralized 
area.  When  the  neutral  zone  is- central,  the  zone  of  motion 
will  be  peripheral  or  marginal  and  vice  versa.  In  the  second 
case  motion  is  with  the  mirror  in  one  unneutralized  area 
(central  or  marginal)  and  against  it  in  the  other;  but  in  the 
former  there  is  but  one  area  of  motion — the  unneutralized 
area.  Figs.  46  and  47  represent  the  double-area  display, 
though  diffusion  is  greater  usually  than  shown  in  either 
case.  It  is  an  effort  of  aberration,  different  areas  of  the 
pupil  having  different  anterior  focal  points.  The  scissors 
movement,  so-called,  is  this  double-area  display,  but  on 
account  of  a  slight  inclination  of  the  two  visual  axes — that 
of  the  observed  and  observing  eye — a  cylindrical  value  is  given 
to  the  dioptry  of  the  observed  eye,  which  causes  the  areas  of 
motion  to  meet  and  separate  along  a  central  line  in  a  plane  at 


THE  STUDY   OF  THE   EYE   BY   SKIASCOPY.  1 59 

right  angles  to  the  plane  of  the  angle  of  inclination  of  the 
visual  axes.  Emmetropia  is  not  indicated  by  the  scissors 
movement,  and  the  more  in  line  the  two  visual  axes  are 
brought  the  less  the  scissors  movement  becomes  manifest 
unless  there  is  a  misplacement  of  the  lens.  Aberration  is  not, 
nor  the  skiascopic  appearances  produced  by  it,  an  anomalous 
phenomenon,  but  one  to  be  expected  and  considered  at  its 
value.  When  the  scissors  movement  is  shown  it  does  not 
show  that  certain  areas  of  the  pupil  are  ametropic  and  others 
are  emmetropic,  but  that  aberration  is  unavoidable  for  so 
near  a  point.  The  human  eye  is  remarkably  free  from  aberra- 
tion, but  really  for  but  two  positions — that  is  at  infinity  and  at 
its  principal  focus — anterior  and  posterior  in  static  refraction. 
But  the  use  of  the  accommodation,  in  dynamic  refraction, 
causes  it  to  be  without  aberration  for  that  anterior  point  to 
which  it  is  accommodated.  But  the  observed  eye  usually  has 
a  lens  of  some  power  before  it  in  a  skiascopic  examination, 
and  if  it  has  no  aberration  the  lens  has,  and  that  gives  us  the 
effects  the  same  as  if  the  dioptric  media  of  the  eye  were  the 
cause  of  it. 

PRODUCING   CASE   2. 

The  primary  work,  whatever  the  initial  appearance,  is  to 
produce  the  conditions  for  case  2.  There  ai^e  two  ways  of 
doing  so:  (i)  by  placing  lenses  in  front  of  the  observed  eye,  and 
(2)  by  changing  the  distance  of  the  observer.  If  the  observed 
eye,  is  either  initially  or  otherwise  ^  D.  myopic,  the  area  of 
reversal  may  be  brought  to  the  observing  eye  by  placing 
+  ^  D.  before  it;  or  it  may  be  produced  by  the  observer  taking 
a  position  2  meters  from  the  observed  eye.  If  the  observed  eye 
is  2  D.  myopic,  the  area  of  reversal  may  be  placed  as  required 
in  case  2,  either  by  giving  it  a  —  i  D.  lens  or  by  moving  the 
observing  eye  to  a  point  |  meter  from  the  observed  eye. 
Either  of  these  methods  would  give  the  primary  result.  Either 
would  show  the  location  of  the  area  of  reversal.  In  one  case 
the  area  of  reversal  is  brought  to  the  eye  at  one  meter  by  a  lens ; 
in  the  other  the  observing  eye  moves  to  the  area  of  reversal. 
If  the  observing  eye  finds  the  area  of  reversal  at  27  in.  from 
the  observed  eye,  a  — 1.5  D.  lens  (40/27)  is  required  for  its 


l6o  THE  STUDY   OF  THE   EYE   BY   SKIASCOPY. 

full  correction.  A  —  .50  D.  lens  would  place  the  area  of 
reversal  at  one  meter,  making  a  secondary  correction  of  —  i 
D.  lens  necessary. 

The  direction  of  the  correction  is  indicated  by  the  direc- 
tion of  motion  of  the  reflex.  If,  with  the  plane  mirror,  it  is 
with  the  light  on  the  face,  plus  lenses  will  be  required  to  in- 
crease such  motion,  and  eventually  to  bring  the  area  of  reversal 
to  the  point  required.  If  motion  is  against  the  mirror  or  light 
on  the  face  minus  lenses  will  be  necessary  to  get  the  primary 
correction.  When  the  primary  correction  is  obtained,  such  a 
secondary  correction  has  to  be  added  as  will  cause  the  area  of 
reversal  to  recede  to  infinity.  For  a  working  distance  of  one 
meter  a  i  —  D.  is  the  secondary  correction. 

The  question  is  often  raised,  and  raised  again,  as  to  what 
effect  the  distance  of  light  or  luminous  area  has  to  do  with  the 
problem.  So  far  as  its  effect  upon  motion,  or  the  direction  of 
motion,  in  the  objective  pupil  is  concerned,  provided  the  pen- 
cils are  allowed  freely  to  evolve  from  the  luminous  area  to  the 
observed  eye,  it  has  no  effect  whatever.  It  may  be  i  meter 
from  the  mirror,  -J  meter,  ^  meter,  or  any  distance.  It  is  the 
distance  between  the  observed  and  observing  eye — the  length 
of  interval  3  only — that  determines  the  secondary  correction 
and  the  lens  required  to  reverse  motion.  A  condensing  lens  of 
less  than  neutralizing  power  may  be  placed  between  the  lumin- 
ous area  and  mirror,  or  a  concave  mirror  may  be  used  so  near 
the  luminous  area  that  it  does  not  transpose  the  pencils,  but 
merely  reduces  the  convex  curvature  of  the  waves  without 
affecting  the  result.  The  use  of  either  of  these  instrumentali- 
ties, however,  gives  a  higher  retinal  illumination  at  area  3. 

But  if  the  lens  or  mirror  transposes  the  incident  pencils, 
focusing  them  anterior  to  the  observed  eye,  there  is  reversal  at 
area  3,  which  reverses  all  the  rules  for  the  use  of  the  plane  mir- 
ror. But  even  this  simply  changes  the  law  of  motion — motion 
with  the  mirror  indicating  myopia,  motion  against  it  indicating 
hyperopia,  emmetropia  or  low  myopia.  It  does  not  change  the 
secondary  correction  of  —  i  D.  for  a  working  distance  of  i 
meter,  —  2D.  for  ^  meter,  —  ^  D.  for  2  meters.  The  emerg- 
ent pencils  of  light,  which  reveal  the  dioptric  condition  of  the 
observed  eye  to  the  observer,  are  independent  of  the  incident 


THE  STUDY   OF  THE   EYE   BY   SKIASCOPY,  l6l 

pencils,  although  they  come  from  an  image  produced  by  inci- 
dent pencils. 

The  distance  of  the  light  from  the  observed  eye  is  a  factor 
in  the  image  at  area  3 — a  factor  in  the  amount  of  diffusion  at 
that  area — a  factor  in  the  development  of  the  banded  appear- 
ance in  astigmatism — a  factor  in  all  effects  upon  incident  pen- 
cils. But  it  is  not  a  factor  in  the  optical  properties  of  the 
emergent  pencils,  except  merely  that  its  image  at  area  3  is  the 
source  of  these  emergent  pencils,  and  the  image  at  area  3  is  the 
original  of  the  image  developed  at  area  4.  The  image  at  area  3 
is  like  any  image  upon  a  screen — a  true  image  displayed  upon 
a  receiving  surface.  But  in  skiascopy  the  definition  is  im- 
paired by  the  eye's  ametropia,  or  because,  if  emmetropic,  the 
accommodation  is  passive,  although  the  luminous  area  is 
at  a  finite  distance.  The  other  peculiar  skiascopic  effects  are 
due  to  the  fact  that  this  imperfect  image  is  examined  through 
the  same  dioptric  media  that  produce  it.  In  hyperopia  and 
emmetropia  there  is  nothing  to  impair  the  view  of  the  observ- 
ing eye,  or  to  prevent  its  getting  a  clear  definition  of  the  image 
upon  this  screen,  for  the  dioptric  media  of  the  observed  eye 
simply  acts  as  a  magnifying  lens.  The  impairment  is  in  the 
image  it  sees  displayed  upon  the  retina  of  the  observed  eye,  and 
due  to  its  hyperopia  in  part,  and  partly  to  the  fact  that  the 
object  imaged  (the  luminous  area)  is  nearer  than  required  to 
be  correctly  focused  at  the  retina.  If  the  observed  eye  is 
hyperopic  that  simply  lessens  its  magnifying  power  or  effect 
upon  the  emergent  pencils,  for  the  dioptric  media  are  nearer 
than  required  for  the  maximum  of  magnification.  In  emme- 
tropia magnification  is  at  the  maximum,  but  the  image  at  area 
3  is  impaired  notwithstanding. 

But  when  the  observed  eye  is  myopic,  every  degree  of  my- 
opia within  that  required  to  exactly  focus  the  incident  pencil* 
upon  the  retina,  improves  the  definition  of  the  luminous  area 
at  area  3.  If,  for  instance,  the  luminous  area  is,  by  way  of  the 
mirror,  i-|  meters  from  the  observed  eye,  which  is  .75  D.  my- 
opic, the  definition  at  area  3  will  be  perfect,  the  image  clear 
and  sharp.  But  the  observing  eye  must  see  this  result  through 
the  same  ametropic  media  that  produces  the  image,  and  since 
it  is  .75  D.  myopic,  the  dioptric  media,  considered  as  a  lens,. 


l62  THE  STUDY   OF  THE   EYE   BY   SKIASCOPY. 

is  a  little  beyond  the  focal  position.  It  therefore  emits  pencils 
from  such  image  already  transposed  and  on  their  way  to  poten- 
tial foci  i^  meters  anterior  to  the  observed  eye,  and  therefore 
posterior  to  the  observing  eye  i  meter  away.  The  observing 
eye  cannot  focus  these  pencils  upon  its  retina,  hence  diffusion 
at  area  4  in  spite  of  the  perfect  definition  at  area  3.  With 
increased  myopia  of  the  observed  eye,  diffusion  develops  al 
area  3  and  increases  at  area  4  until  the  maximum  of  diffusion 
is  reached.  But  the  distance  of  the  light  from  the  mirror  has 
nothing  to  do  with  diffusion  at  area  4. 

ABSOLUTE  CONDITION. 

In  skiascopy,  as  usually  practiced,  the  first  view  of  the 
eye  does  not  show  whether  it  is  myopic,  hyperopic  or  emme- 
tropic, if  motion  is  with  the  mirror.  It  may  be  hyperopic,  em- 
metropic or  slightly  myopic.  It  would  be  better  to  ascertain 
the  absolute  condition — whether  it  is  emmetropic,  myopic  or 
hyperopic — at  the  first  glance.  This  may  be  done  by  the  follow- 
ing simple  and  direct  method : 

If  the  Avorking  distance  is  one  meter,  place  a  +  i  D.  sph. 
lens  in  the  rear  cell  of  the  trial  frame  to  start  with;  or  if  work- 
ing at  2  meters,  place  a  +  ^  D.  sph.  lens  in  the  cell;  or  if  work- 
ing at  ^  meter,  place  a  +  2  D.  sph.  lens  in  the  cell.  If  the  eye 
to  be  examined  is  emmetropic  this  secondary  lens  wall  bring 
the  area  of  reversal  to  the  observing  eye,  and  the  appearances 
in  case  2  will  at  once  be  manifest.  If  the  eye  is  liyperopic, 
motion  will  be  with  the  plane  mirror  still,  for  its  area  of  re- 
versal will  be  more  than  one  meter  anterior  to  the  observed, 
and  therefore  posterior  to  the  observing  eye.  If  the  eye  to  be 
examined  is  myopic,  even  but  .25  D.,  motion  will  be  against  the 
plane  mirror,  for  the  +  i  D.  lens  will  make  it  1.25  D.  myopic, 
and  the  area  of  reversal  will  be  but  ^  of  a  meter  anterior  to  the 
observed  eye,  and  therefore  anterior  to  the  observing  eye,  or 
between  the  observed  and  the  observing  eyes. 

But  another  great  advantage  of  this  method  is  that  the 
lens  that  brings  out  the  appearances  of  case  2,  or  brings  the 
area  of  reversal  to  the  observing  eye,  is  the  full  correction  with- 
out subsequent  additions  or  subtractions.  This  is  evident  from 
the  fact  that  the  lens  in  the  back  cell  is  not  taken  into  account, 


THE   STUDY    OF  THE   EYE   BY   SKIASCOPY.  163 

but  is  simply  "left  out"  of  the  calculation.  To  leave  out  a 
+  I  D.,  +  ^  D.  or  +  2  D.  lens  actually  before  the  eye  when 
motion  is  neutralized  is  the  same  as  adding  a  —  i  D.,  —  i  D. 
or  —  2D.  to  the  primary  correction.  This  plan  is  simple,  opti- 
cally correct  and  very  convenient.  It  is  probably  practiced  by 
many  skiascopists,  although  we  have  not  seen  it  recommended 
as  a  method  in  any  text-book. 

THE  CONCAVE  MIRROR. 

The  concave  mirror  can  also  be  conveniently  employed 
without  complicating  the  rules  of  motion  for  plane  mirrors. 
This  may  be  done  by  using  the  ordinary  concave  mirror  of  25 
centimeters  (10  in.)  focus  at  less  than  10  inches  from  the  lumin- 
ous area — that  is,  by  bringing  the  luminous  area  to  a  point,  say 
about  8  inches  from  the  mirror  or  observing  eye.  The  incident 
pencils  reaching  the  mirror  would  be  composed  of  waves  of 
(at  8  in.)  a  curvature  of  +  5  Cm.  As  a  concave  mirror  of  25 
centimeters  has  a  power  equivalent  to  a  four  diopter  lens,  it 
would  not  transpose  the  pencils  but  reflect  them  in  convex 
waves  or  diverging  rays  to  the  observed  eye.  The  major  pen- 
cils producing  the  "light  on  the  face"  would  be  more  intense, 
on  account  of  the  action  of  the  mirror,  and  the  minor  pen- 
cils admitted  by  the  pupil  would  partake  of  such  increased  in- 
tensity. The  reflex  would  be  made  brighter  without  involving 
any  of  the  skiascopic  factors  of  motion  or  changing  the  rule  for 
plane  mirrors.  In  efifect  it  would  remove  the  luminous  area  to 
a  greater  distance,  by  placing  the  center  of  curvature  of  each 
series  of  waves  at  a  greater  distance,  and  this  would  sharpen 
the  definition  with  approach  to  the  full  correction  by  eliminat- 
ing diffusion.  The  use  of  the  secondary  lens  in  the  back  cell 
would,  however,  increase  diffusion  at  area  3,  for  that  lens  is 
not  a  part  of  the  full  correction,  but  is  left  out  and  ignored. 

This  method  would  correspond  closely  to  the  use  of  a  neu- 
tralizing lens  in  the  skiascopic  chimney  heretofore  described, 
and  might  prove  a  more  simple  solution  of  securing  an  ac- 
ceptable static  test,  or  test  by  definition  rather  than  by  motion. 
11 


CHAPTER  VIII. 


THE  STUDY  OF  THE  EYE  BY  SKIASCOPY.      UNSYMMETRICAL  AME- 
TROPIA.    REGULAR  ASTIGMATISM.      IRREGULAR  ASTIG- 
MATISM.     STATIC    AND    DYNAMIC    PROPERTIES. 
PATHOLOGICAL  CASES. 


AN  eye  is  a  positive  optical  instrument.  It  is  positive  in  all 
•  meridians.  An  astigmatic  eye  is  simply  one  having 
greater  dioptric  pov^er  in  some  meridians  than  in  others. 
In  regular  astigmatism  there  is  not  only  a  meridian  of  greatest 
and  a  meridian  of  least  dioptric  power,  but  all  intermediaze 
meridians  have  intermediate  power  in  proportion  to  their 
nearness  to  the  meridian  of  greatest  power.  The  merid- 
ians of  greatest  and  least  power  are  at  right  angles  to 
each  other,  for  the  astigmatism  is  due  to  a  cylinder  effect 
of  the  dioptric  media,  due  usually  to  a  toric  curvature  of  the 
cornea,  or  greater  curvature  in  one  and  less  curvature  in  other 
of  its  meridians,  the  two  being  at  right  angles  to  each  other, 
than  any  intermediate  meridian.  The  intermediate  meridians 
then  have  an  intermediate  degree  of  curvature  proportional  to 
their  nearness  to  the  meridian  of  greatest  curvature. 

It  is  proved  that  an  intermediate  meridian  of  piano-cyl- 
inder has  a  curvature  proportional  to  the  square  of  the  sine  of 
its  angle  to  the  axis  of  the  cylinder  divided  by  the  radius  of 
curvature.  That  is,  if  the  sine  of  the  angle  as  measured  by  the 
radius  be  squared,  the  result  is  the  ratio  of  the  given  merid- 
ian's curvature  to  the  curvature  of  the  meridian  of  greatest 
curvature.  For  instance,  if  the  curvature  of  a  piano-cylinder 
is  lo  Cm.,  or  its  radius  of  curvature  is  4  in.,  a  meridian  45' 
from  the  axis  of  the  cylinder  would  have  a  curvature  of  |  of 

164 


THE  STUDY   OF  THE   EYE   BY   SKIASCOPY. 


i6= 


lo  Cm.  =  5  Cm.,  or  a  radius  of  curvature  of  8  in.  A  meridian 
at  30°  from  the  axis  of  the  cylinder  has  a  curvature  of  ^  of  10 
Cm.  =  2^  Cm.,  or  a  radius  of  curvature  of  16  in.  A  meridian  at 
15°  from  the  axis  has  a  curvature  of  .067  of  10  Cm.  =  .67  Cm.,  or 
a  radius  of  curvature  of  about  60  in.  The  ^,  ^  and  .067  Cm.  are 
each  the  square  of  the  sine  of  their  respective  angles  as  meas- 
ured by  the  radius.  The  sine  of  30°  is  ^  of  a  chord  of  60°,  which 
is  equal  to  the  radius;  hence  the  sine  of  30°  =  ^  radius,  and  Q)' 
=  ■^.  The  sine  of  45°  is  -J  the  chord  of  90°,  which  makes 
the  chord  and  radius  each  bisect  the  other  at  right  angles. 
Hence  the  sine  is  1/  ^  R2  and,  since  the  radius  is  taken  as  unity, 
1/  ^.  The  square  of  ]/  i  is  of  course  ^.  The  ratio  of  any  sine, 
or  the  sine  of  any  angle  to  the  radius  is  found  in  tables,  as  the 
calculation  for  small  angles  would  be  exceedingly  tedious. 


+  77  D 

"-?$ 

i»-"~ 

0 

/ 

/   >\  (''*■  '''^)  ^ 

\.^jm^^ 

S 

m 

rs^:  \ 

'^"SK^  \ 

^^j 

f  .,Z!b> 

«^ 

y 

Fig.  48. 


Applying  the  above  principle  to  the  dioptry  of  an  astig- 
matic eye  if,  for  instance,  the  dioptry  of  the  veitical  meridian 
is  +  ?r  D.,  and  that  of  the  horizontal  is  +  (  -  +  i  )  D.,  the 
horizontal  has  i  D.  greater  power  than  the  vertical.  But  the 
45th  and  135th  meridians  have  each  +  (  -^  +  2  )  D.,  and  these 
two  meridians  are  perpendicular  to  each  other  the  same  as  90° 
and  o,  and  ametropia  is  symmetrical  for  these  two  meridians. 
However,  meridian  60°,  30°  from  90°,  has  a  dioptry  of  + 
( TT  +  I)  D.,  and  meridian  150°,  at  right  angles  to  60°,  has  a 
dioptry  of  +  (  -  -f  f  )  D.,  for  it  is  60°  from  90°,  or  30°  from 
180°.    Its  dioptry  is  therefore  i  D.  less  than  180°  =  +  ( 7:  +  f ) 


i66 


THE   STUDY    OF  THE   EYE   BY   SKIASCOPY. 


D.    Fig.  48  represents  the  meridians  here  described,  showing 
the  dioptric  value  or  power  of  each. 

A  case  of  the  kind  last  described  is  called,  in  the  vernacu- 
lar of  opticians,  simple  myopic  astigmatism  of  i  diopter,  and 
would  be  produced  artificially  in  an  emmetropic  eye  by  a  + 
I  D.  cyl.  ax.  90°.  The  eye  is  emmetropic  in  but  one  meridian 
— the  vertical — where  its  dioptric  power  is  +  ~  D.  It  is  my- 
opic in  every  other  meridian,  from  the  90th  to  the  i8oth  in 
either  direction,  being  in  the  latter  -f  (  -  -|-  i  )  D.  The 
amount  of  myopia  in  the  oblique  meridian  increases  regularly 
from  o  to  I  D.     Now,  if  this  eye,  which  may  be  naturally  or 


(u-2)D 


Fig.  49. 


artificially  astigmatic  i  D.  is  supplied  with  a  —  i  D.  spherical 
lens,  the  lens  will  neutralize  the  horizontal  meridian,  but  pro- 
duce hyperopia  in  the  vertical  meridian — that  is,  the  eye  will 
become  +  -  D.  in  the  horizontal,  but  +  (  ~  —  i  )  D.  in  the 
vertical  meridian,  as  shown  in  Fig.  49.  But  this  same  ef¥eci. 
may  be  produced  in  an  emmetropic  eye  by  placing  a  —  i  D. 
cyl.  ax.  180°  before  it.  By  adding  a  —  i  D.  sphere  to  the  first 
case  it  has  been  metamorphosed  from  n  case  of  simple  myopic 
astigmatism  into  one  of  simple  hyperopic  astigmatism.  Note 
also  the  efifect  at  the  intermediate  meridians. 

Now,  if  instead  of  a  —  i  D.  sphere  a  +  i  D.  had  been 
added  to  the  original  case,  the  vertical  meridian  would  have 
become   -f   (  r   —    i  )    D.,   and   the   horizontal    would   be   H- 


THE   STUDY    OF  THE   EVE   BY    SKIASCOPY. 


107 


(::  -f  2)  D.,  as  shown  in  Fig.  50.  This  is  a  case  of  so-called 
compound  myopic  astigmatism.  So,  also,  if  a  —  2D.  sph.  is 
added  to  the  original  case  the  vertical  meridian  becomes    r 


i-(--n)  D 


(  :T  +  I  /z  j  D 

-  +  I  %)  0 


+  (k  +  2J  D 


Fk;.  5'. 

(-  —  2)  D.,  and  the  horizontal  +  (  ~  —  1  )  D..  a  case  of 
compound  hyperopic  astigmatism,  as  shown  by  Fig.  51.  But 
the  astigmatic  element  remains  unchanged  by  the  spherical 
lenses.  To  produce  compound  astigmatism  in  an  emmetropic 
eye  a  compound  lens  would  Ijc  required.    That  is,  to  produce 


Fn:.  PI. 

-[-(-+    I )   D.  in  the  vertical  and  +  (  ~  +   2  )  D.  in  the  hori- 
zontal of  an  emmetropic  eye,  a 

(i)  +  I  D.  sph  ~  +  I  D.  cyl.  ax.  90° 
would  be  necessary.     And  to  produce  +  (,  ~  —  2  )  D.  in  the 
vertical  and  +  ( ~  —   i  )  D.  in  the  horizontal  of  an  emme- 
tropic eye,  a 


1 68 


THE   STUDY   OF  THE   EYE   BY   SKIASCOPY. 


(2)  —  I  D.  sph.  C  —  I  D-  cyl.  ax.  180° 

would  be  necessary.     Other  compounds  would  produce  the 
same  result,  as 

(3)  +  2  D.  sph.  C  —  I  D.  cyl.  ax.  180°  for  (i),  or 

(4)  —  2D.  sph.  3  +  I  D.  cyl.  ax.    90°  for  (2), 

it  is  true,  but  (i)  and  (2)  embody  the  least  curvature  of  the 
lens  surfaces. 


+  {n-'/i)D 


+  (rt  +  /4)  0 


+  (rT-f  ^2^0 


Fig.  52. 

But  the  original  case  +  -  D.  in  the  vertical  and  + 
(::■  +  i)  D.  in  the  horizontal)  might  as  readily  be  turned  into 
a  case  of  mixed  astigmatism  by  using  a  spherical  of  less  power 
than  the  degree  of  astigmatism.  If,  for  instance,  a  —  .5  D. 
sph.  were  used,  the  45th  and  135th  meridians  would  be  neu- 
tralized, but  the  horizontal  would  become  +  (  ~  -{-  ^  )  D.,  or  -J 
D.  myopic,  while  the  emmetropic  vertical  meridian  would  be- 
come +  (  ~  —  I)  D.  or  ^  D.  hyperopic.  Fig.  52  illustrates 
the  last  condition. 

In  all  of  these  changes  brought  about  by  adding  a  spheri- 
cal to  an  astigmatic  eye  the  intermediate  meridians  are  changed 
in  power  according  to  the  principle  enunciated  at  the  begin- 
ning of  the  chapter  and  as  shown  by  the  different  figures.  In 
the  last  case  meridians  45°  and  135°  become  emmetropic,  but 
they  have  had  the  same  dioptry  all  through  the  various 
changes.  But  the  principal  meridians  and  all  the  intermediate 
meridians  are  unaltered  in  their  relative  dioptry. 

It  takes  a  cylinder  to  neutralize  the  different  meridians — 
each  in  proportion  to  its  need,  for  a  cylinder  produces  all  these 


THE   STUDY    OF  THE    EYE   BY   SKIASCOPY.  169 

conditions  in  an  emmetropic  eye.  A  spherical  lens  is  required 
to  neutralize  real  myopia  or  hyperopia,  but  it  cannot  take  out 
an  astigmatic  element.  A  cylinder  neutralizes  astigmatism — 
makes  the  meridians  agree — but  it  does  not  neutralize  real  my- 
opia or  hyperopia.  The  cylinder  harmonizes  not  only  the  two 
principal  meridians  but  all  the  intermediate  meridians.  The 
one  emmetropic  meridian  does  not  need  assistance  from  the 
cylinder.  It  is  therefore  so  placed  that  the  axis  of  the  cylinder 
and  the  emmetropic  meridian  coincide.  The  power  of  the  cyl- 
inder is  then  exercised  where  it  is  needed — not  only  in  the 
one  principal  but  all  the  intermediate  meridians.  If  neither  of 
the  principal  meridians  are  emmetropic,  a  spherical  lens  will 
correct  one  of  them  and  a  cylinder  will  then  correct  the  others. 

It  is  seen  from  the  above  analysis  that  astigmatism  is  not 
really  hyperopic  or  myopic,  or  compound  or  mixed.  Regular 
astigmatism  is  a  mere  proportionate  difference  in  the  power  of 
different  meridians.  It  is  the  hyperopia  or  myopia  that  is 
astigmatic,  rather  than  that  the  astigmatism  is  hyperopic  or 
myopic.  Simple  astigmatic  myopia  and  compound  astigmatic 
myopia  would  be  more  significant  expressions  than  simple  or 
compound  myopic  astigmatism.  Mixed  astigmatism  is  really 
mixed  myopia  and  hyperopia  rather  than  mixed  astigmatism. 
The  astigmatism  is  not  the  least  rfiixed  in  any  case,  but  my- 
opia and  hyperopia  prevail  in  different  meridians,  and  they  may 
be  said  to  be  mixed.  Take  out  the  astigmatism  and  the  my- 
opia or  hyperopia  may  be  increased  instead  of  lessened.  If  an 
eye  is  +  (  ^^  +  3  )  D.  in  the  vertical  and  +  (  -  +  4  )  D.  in 
the  horizontal,  a  +  i  D.  cyl.  ax.  180°,  or  a  —  i  D.  cyl.  ax.  90° 
will  take  out  the  element  of  astigmatism.  The  former  will  add 
to  the  myopia  in  the  vertical  and  the  latter  will  subtract  from 
the  myopia  in  the  horizontal.  One  will  make  the  eye  4- 
(:r  +  4)  D.  in  all  meridians;  the  other  will  make  it  + 
( TT  -f-  3  )  D.  in  all  meridians.  There  is  then  a  certain  sym- 
metry to  regular  astigmatism. 

We  sometimes  find  cases  that  follow  certain  rules  of  sym- 
metry, but  which  yet  appear  dififerent  than  regular  one-cyl- 
inder astigmatism.  For  instance,  we  find  an  eye  that  is  + 
(tt  +  5)  D.  in  120°  and  +  (~  +7  )  D.  in  60°.  As  these 
two  meridians  are  not  at  right  angles  a  —  5  D-  sphere  which 


170  THE  STUDY   OF  THE   EYE   BY   SKIASCOPY. 

neutralizes  120°  leaves  60°  at  +  (  ~  +  2)  D.  But  a  —  2D. 
cyl.  ax.  150°,  which  neutralizes  60°,  has  a  power  oi  ^  oi  —  2D. 
at  120°,  30°  from  its  axis,  and  therefore  —  5  D.^  3  —  2  D.^  ax. 
150°  will  not  correct  the  case.  If  we  use  a  —  7  D.^  3  +  2  D.<^ 
ax.  30°  it  will  neutralize  120°,  but  will  leave  60°  +  ("  +  .5  ) 
D.  in  the  same  manner.  We  may  find  cross  cylinders  that  will 
neutralize  both  meridians,  and  therefore  all  meridians,  axes 
respectively  at  30°  and  150°.  We  may  determine  the  dioptry  of 
each  cylinder: 

Let  X  =  diopter  of  cyl.  ax.   150°. 
Let  y  =  diopter  of  cyl.  ax.     30°. 

Then,  according  to  rule,  we  have  the  equations: 

(i)  X  +  i  y  =  7 
(2)  y  +  i  X  =  5 

in  which  the  values  of  .r  and  y  are  found  to  be  6.133+  and 
4.466+  respectively.    Therefore  cross  cylinders: 

— 4.466  D.  ax.  30°  C  —  6.133+  D.  ax.  150° 

will  neutralize  both  and  all  meridians. 

But  the  above  cross  cylinders  can  be  reduced  to  a  simple 
sphero-cylinder,  the  cylinder's  greatest  dioptric  value  being 
neither  at  60°  nor  120°,  and  therefore  its  axis  at  neither  30°  nor 
150°.  In  other  words  the  above  meridians  (60°  and  120'')  are 
not  the  chief  but  two  intermediate  meridians,  and  two  chief 
or  principal  meridians  of  an  astigmatic  eye  cannot  be  at  any 
other  angle  to  each  other  than  90  degrees  in  regular  astigma- 
tism. In  the  cross  cylinders  above  meridian  75°,  for  instance, 
has  a  dioptric  value  of  -J-  of  y,  and  loses  but  .067  of  the  diop- 
tric value  of  ,r: 

^     of  4.466  =  2.233 
.933  of  6.133  =  5.722 

7-955 

Its  diopter  is  therefore  7.955,  or  more  than  either  60°  or  120'. 
What  lenses  do  to  change  the  dioptry  of  the  eye  in  cases  cited 
the  accommodation  is  constantly  doing,  but  no  use  of  the  ac- 
commodation afifects  the  element  of  astigmatism.  It  remains 
constant  in  all  the  changes. 


THE   STUDY   OF  THE   EYE   BY   SKIASCOPY.  I7I 

SKIASCOPIC  APPEARANCES. 

Under  a  skiascopic  examination  astigmatism  reveals  itself 
unmistakably,  for  motion  follows  the  rule  of  its  meridian,  and 
is  therefore  different  in  different  meridians,  the  same  as  in  an 
examination  of  two  eyes  having  ametropia  of  different  kinds 
or  degrees  shows  the  differences  for  the  two  eyes,  an  astigmatic 
eye  giving  you  the  resultant  of  the  two  motions.  In  a  case  of 
astigmatism  if  the  mirror  is  tilted  across  one  of  the  principal 
meridians,  at  right  angles  to  it,  the  area  of  light  on  the  face 
moves  along  the  other  principal  meridian,  and  motion  in  the 
pupil  shows  the  dioptric  condition  of  the  latter.  If  there  is  dis- 
tinct motion  it  must  be  with  or  against  the  mirror,  and  there- 
fore shows  whether  the  meridian  is  myopic  or  hyperopic — 
that  is,  with  the  secondary  lens  in  the  rear  cell  as  heretofore 
described.  The  speed  of  motion  will  be  of  special  value,  for  by 
tilting  the  mirror  in  opposite  meridians  and  noting  the  differ- 
ence of  speed  of  motion  an  idea  of  the  degree  of  astigmatism,. 
if  there  is  any,  will  be  obtained. 

But  the  skiascopist  does  not  know,  to  start  with,  whether 
there  is  astigmatism  or  not,  and  if  there  is  astigmatism,  he 
doesn't  know  what  the  direction  of  the  principal  meridians 
may  be.  Hence  he  is  unable  to  tilt  the  mirror  in  either  of  the 
principal  meridians  off  hand.  He  may  happen  to  do  so,  for  in 
a  great  majority  of  cases  the  90°  and  180°  meridians  are  the 
principal  meridians,  but  he  is  quite  likely  not  to  do  so.  If  the 
mirror  is  tilted  so  as  to  cause  the  light  on  the  face  to  move 
along  an  intermediate  meridian,  it  may  show  more  rapid  mo- 
tion than  one  and  less  rapid  motion  than  the  other  chief  me- 
ridian, or  it  may  be  an  emmetropic  meridian  and  show  no  mo- 
tion. But  if  it  shows  motion,  the  adjacent  meridians,  some 
of  greater  and  some  of  less  power,  will  give  a  peculiar  swirling 
effect  to  the  image  or  motion  to  the  reflex,  for  on  one  rotary 
side  refraction  will  tend  to  make  the  reflex  move  faster  while 
in  the  other  it  tends  to  make  it  move  slower.  The  effect  is  to 
make  motion  in  the  pupil  conform  with  the  principal  meridian 
in  which  motion  is  most  rapid,  whether  the  mirror  is  tilted 
along  that  meridian  or  not.  The  principal  meridian  may  be 
found  by  tilting  the  mirror  in  the  meridian  that  allows  the 
reflex  to  move  with  or  against  the  light  on  the  face  instead  of 


172  THE   STUDY   OF  THE   EYE   BY   SKIASCOPY. 

at  an  oblique  angle  to  it.    But  the  principal  meridians  are  more 
distinctly  displayed  by  developing  the  banded  appearance. 

Astigmatism  is  clearly  indicated  by  the  dififerent  degrees 
of  motion  of  the  reflex  in  different  meridians.  This  is  mani- 
fest whether  motion  is  with  or  against  the  mirror  in  all  merid- 
ians. It  is  clearly  manifest,  of  course,  when  motion  in  one 
principal  meridian  is  with  the  mirror  and  in  the  other  against 
the  mirror.  In  that  case  there  is,  necessarily,  in  regular  astig- 
matism one  neutral  meridian,  an  intermediate  meridian  some- 
where between  the  two  principals,  all  meridians  in  one  direc- 
tion (one  rotary  direction)  being  of  higher  and  in  the  other  of 
lower  power.  But  astigmatism  is  more  clearly  marked  when 
one  of  the  principal  meridians,  or  motion  in  one  of  them,  is 
neutralized,  for  then  diffusion  is  at  the  maximum  in  that  me- 
ridian, for  the  area  of  reversal  of  that  principal  meridian  is  at 
the  fixed  plane  of  reversal  of  the  observing  eye.  There  is  usu- 
ally more  or  less  diffusion  in  the  other  meridian,  but  this 
may  be  minimized  by  placing  the  luminous  area  at  the  other 
principal  area  of  reversal,  or  at  the  same  distance,  by  way  of 
the  mirror,  from  the  observed  eye  as  the  other  principal  area 
of  reversal.  When  one  principal  meridian  is  thus  neutralized 
the  reflex  extends,  in  that  meridian,  from  one  pupillary  mar- 
gin to  the  other.  This  is  the  meridian  of  greatest  diffusion. 
But  unless  the  other  meridian  is  nearly  focused  at  area  4,  and 
therefore  without  much  diffusion,  the  banded  appearance  is  not 
distinct.  Figs.  53  and  54  illustrate  an  elongation  of  the  reflex 
in  one  meridian,  the  elongation  being  in  the  meridian  of  great- 
est diffusion,  or  the  meridian  whose  area  of  reversal  is  nearest 
the  fixed  plane  in  the  observing  eye.  It  cannot  be  said  which 
of  these  meridians  is  most  myopic,  for  that  depends  upon 
whether  the  area  of  reversal  of  intermediate  and  area  of  re- 
versal of  the  other  principal  meridians  are  anterior  or  posterior 
to  the  observing  eye. 

THE   BANDED   APPEARANCE. 

The  optical  principles  upon  which  the  banded  appearance 
depends  are  not  difficult  to  understand,  but  unless  one  under- 
stands that  there  is  an  area  of  reversal  for  each  principal  me- 
ridian (as  well  as  for  all  intermediate  meridians),  one  of  which 


Fig.  53.     Page  172. 


Fig.  54.     Page  172. 


Fig.  .55      Page  174. 


Fig.  56.     Page  174. 


:jfriOrx 


Fig   57.     Page  179. 


Fig.  ->H.     Page  179. 


THE   study'  of  the   EYE   BY   SKIASCOPY.  I73 

is  nearer  the  observed  eye  than  the  other,  it  is  hard  to  explain. 
To  bring  up  the  banded  appearance  most  strikingly  it  is  neces- 
sary that  the  observing  eye  be  at  one  of  these  principal  areas 
of  reversal,  and  the  luminous  area  (or  the  virtual  image  of  it) 
be  at  the  other.  In  the  use  of  the  plane  mirror  it  is  necessary 
that  the  observing  eye  be  at  the  area  of  reversal  of  the  more 
myopic  meridian  of  the  observed  eye,  for  the  luminous  area 
is  necessarily  farther  from  the  observed  eye,  by  v/ay  of  the 
mirror,  than  the  observing  eye.  If  the  eye  under  examination 
is  (artificially  or  naturally)  one  diopter  myopic  in  the  vertical 
and  f  D.  in  the  horizontal,  the  area  of  reversal  for  the  vertical 
meridian  will  be  one  meter  in  front  of  it,  but  the  area  of  rever- 
sal for  the  horizontal  will  be  i^  meters  in  front  of  it. 

Now,  if  the  observing  eye  is  at  one  meter  it  will  be  at  the 
area  of  reversal  for  the  vertical  meridian;  and  if  the  luminous 
area  is  ^  meter  in  front  of  the  mirror,  the  virtual  image  in  the 
mirror  will  be  i|  meters  from  the  observed  eye,  or  at  the  other 
area  of  reversal.  The  pencils  from  the  luminous  area,  i^ 
meters  away,  by  way  of  the  mirror,  will  be  accurately  focused 
by  the  observed  eye  in  the  horizontal;  but  the  vertical  meridian 
will  focus  them  forward  of  area  3,  producing  dififusion  at  the 
retina  in  the  vertical  meridian,  the  meridian  of  inaccurate 
focusing.  The  figure  on  the  retina  will  be  elongated  in  the  ver- 
tical because  of  such  dififusion,  but  it  Will  amount  there  to  but 
a  trifle  for  ^  of  a  diopter's  difiference.  But  before  creating  an 
efifect  at  area  4  it  is  necessary  that  emergent  pencils  start  from 
this  image  and  reach  area  4,  and  to  do  that  they  must  pass 
through  the  dioptric  media  of  the  observed  eye,  as  well  as 
through  the  dioptric  media  of  the  observing  eye. 

What  then  is  the  result  of  these  emergent  pencils  passing 
through  the  dioptric  media  of  the  observed  eye?  In  the  verti- 
cal meridian  they  are  transposed  and  focused  at  one  meter.  In 
the  horizontal  meridian  they  are  transposed  and  focused  at  ij 
meters.  What  would  be  the  result  if  a  screen  intercepted  them 
at  one  meter?  In  the  vertical  meridian  they  would  be  focused 
at  the  screen,  but  in  the  horizontal  they  would  not  be.  There 
would  then  be  displayed  at  the  screen  an  image  of  the  figure 
at  area  3,  elongated  horizontally  by  dififusion  but  accurate 
vertically — a  copy  of  its  original  at  area  3,  but  enlarged  to  J 


174  THE   STUDY   OF  THE   EYE   BY   SKIASCOPY. 

the  extent  of  the  himinous  area  plus  the  dififnsion  in  the  vertical 
at  area  3,  for  the  correct  focusing  of  the  vertical  does  not  elim- 
inate the  diffusion  of  its  original  at  area  3.  The  f  is  the  ratio- 
of  distances  of  the  luminous  area  and  the  screen  from  the  ob- 
served eye.  But  instead  of  having  a  screen  at  this  point  we 
have  the  observing  eye  with  its  emmetropic  media.  What  can 
and  does  it  do  with  these  pencils  focused  at  its  fixed  plane 
of  reversal — practically  the  cornea — in  the  vertical;  but  on 
their  way  to  their  potential  foci  |  meter  farther  on  in  the  hori- 
zontal? The  observing  eye  can  do  practically  nothing  in  the 
vertical.  It  has  no  dioptric  capacity  or  power  upon  waves  of 
light  whose  curvature  is  infinite.  It  cannot  reduce  diffusion  in 
the  vertical.  But  in  the  horizontal  it  has  some  power,  for  the 
waves  are  —  2  Cm.  in  that  meridian  only.  It  cannot  focus 
them,  even  in  that  meridian,  upon  area  4,  but  it  will  focus  them 
slightly  forward  of  area  4.  Result:  at  area  4  there  will  be  the 
maximum  of  diffusion  in  the  vertical  and  the  minimum  of  dif- 
fusion in  the  horizontal.  And  upon  the  imaged  pupil  at  area  4 
a  band  of  light  in  the  vertical  wall  extend  from  margin  to  mar- 
gin. The  observer  projects  this  result  at  area  4  out  into  the 
world,  and  the  "banded  appearance,"  so-called,  is  seen  in  the 
objective  pupil.  The  band  is  in  the  meridian  of  greatest  dif- 
fusion, in  this  case  the  meridian  of  greatest  myopia.  See  Figs, 
55  and  56, 

To  produce,  in  this  eye,  the  band  in  the  other  principal 
meridian,  it  would  be  necessary  for  the  observing  eye  and  the 
luminous  area  to  change  places — for  the  observing  eye  to  be 
at  the  area  of  reversal  most  distant  from  the  observed  eye  while 
the  luminous  area  is  at  the  other,  the  nearest  area  of  reversal. 
But  to  produce  these  conditions  the  luminous  area  would  need 
to  be  forward  of  the  mirror — nearer  the  observed  eye  than  it  ;s 
to  the  observing  eye.  As  with  a  plane  mirror  the  distance  of  the 
light  counts,  from  the  luminous  area  to  the  mirror  and  thence 
back  to  the  observed  eye,  it  is  evident  the  plane  mirror  would 
not  do.  But  with  a  concave  mirror  focusing  the  luminous  area 
between  the  observed  and  observing  eyes  and  producing  an 
aerial  image  there,  which  is  the  immediate  source  of  the  in- 
cident  pencils  reaching  the  observed  eye,  the  luminous  area 
would  be  forward  (instead  of  back)  of  the  mirror,  and  there- 


THE   STUDY    OF   THE   EYE   BY    SKIASCOPY.  I75 

fore  nearer  to  the  observed  eye  than  the  observing  eye  is.  All 
that  would  be  necessary  would  be  to  get  the  focal  area  of 
the  mirror  and  area  of  reversal  anterior  to  the  observing  eye 
together — the  same  distance  from  the  observed  eye.  Usually 
a  little  adjusting  of  distances  will  do  this.  It  is  only  necessary 
to  bear  in  mind  that  the  nearer  the  concave  mirror  is  to  the 
luminous  area  the  farther  away  its  focal  area  must  be.  If  it 
is  nearer  the  luminous  area  than  its  principal  focal  length  it  will 
have  no  positive  focal  area  and  produce  no  real  image,  for  it 
will  not,  in  that  position,  be  able  to  transpose  the  pencils.  It 
must  therefore  be  farther  from  the  luminous  area  than  such 
•distance.  If  the  observer  has  the  area  of  reversal  of  the  least 
myopic  meridian  at  his  eye  he  must  not  alter  his  position,  but 
the  adjusting  of  distances  must  be  made  by  moving  the  light 
so  as  to  change  the  position  of  the  focus  of  the  mirror  between 
observed  and  observing  eyes. 

LIMITATIONS  IN  BOTH  CASES. 

There  are  then  limitations  in  bringing  out  both  bands, 
unless  one  is  provided  with  both  kinds  of  skiascopic  mirrors. 
For  instance,  if  an  eye  has  3  diopters  of  astigmatism  and  both 
meridians  are  hyperopic,  one  i  D.  and  the  other  4  D..  a  +  2  D. 
lens  will  bring  one  area  of  reversal  to  i  meter,  but  there  will  be 
no  area  of  reversal  for  the  other  meridian,  which  is  still  2  diop- 
ters hyperopic.  A  +  5  D.  lens  will  bring  the  more  hyperopic 
meridian  to  reversal  at  i  meter,  but  the  other  meridian  will  re- 
A^erse  at  10  in.  from  the  observed  eye.  The  observing  eye  may 
be  moved  to  this  point,  and  the  light  be  placed  30  in.  from  the 
mirror,  or  30  +  10  =  40  in.  from  the  observed  eye,  and  the 
banded  appearance  be  developed,  but  it  will  be  complicated 
with  marginal  aberration.  It  would  be  better  in  such  a  case 
to  use  the  concave  mirror,  for  if  an  ordinary  25  centimeter 
concave  mirror  were  used,  the  observing  eye  being  at  one 
meter,  to  place  the  immediate  source  of  light,  the  focal  area  of 
the  mirror,  at  10  in.  from  the  observed  eye  and  30  in.  from  the 
observing  eye.  the  light  would  be  placed  at  the  point  conjugate 
to  30  in.,  or  at  15  in.  A  25  centimeter  mirror  is  a  +  4  D.  mir- 
ror. It  has  4  diopters  of  power.  If  the  reflected  pencils  are 
to  focus  at  30  in.,  they  must  be  reflected  as  40/30  =  —  i;^  Cm. 


1/6  THE   STUDY    OF  THE    EYE   BY    SKIASCOPY. 

waves.  But  a  25  centimeter  mirror  will  focus  neutral  waves  at 
10  in.,  or  do  4  diopters  of  work.  The  mirror  must  then  be 
given  4  —  i^  =  2|  diopters  of  work  upon  incident  pencils,  or 
have  pencils  of  +  2f  Cm.  waves  to  reflect.  The  points  of  origin 
of  such  v^raves  must  be  40/2!  =  15  in.  distant.  Of  course  the 
amount  of  astigmatism  is  not  known  to  start  with,  but  if  it 
appears  to  be  considerable — more  than  one  diopter — the  con- 
cave mirror  can  be  used  to  better  advantage  in  developing  the 
band,  especially  for  a  working  distance  of  one  meter. 

But  for  low  degrees  of  astigmatism  the  concave  mirror  is 
inadequate.  If  the  light  is  brought  nearer  than  13  in.  to 
the  25  centimeter  mirror,  its  focal  area  is  beyond  the  observed 
eye.  If  the  light  is  at  infinity  its  focal  area  is  10  in.  in  front  of 
the  mirror  or  30  in.  from  the  observed  eye,  and  cannot  be 
brought  nearer  the  mirror.  But  neither  of  these  positions 
would  do,  for  the  focal  area  must  be  at  one  of  the  areas  of 
reversal  and  cannot  be  at  or  beyond  the  observed  eye,  but 
must  be  between  the  observed  and  observing  eye;  and  the 
light  cannot  be  at  infinity,  but  must  be  within  one  meter  to 
give  sufBcient  illumination.  With  the  light  at  one  meter  the 
focal  area  of  the  mirror  would  be  13  in.  in  front  of  the  mirror, 
or  27  in.  from  the  observed  eye.  So  that  if  the  observed  eye 
had  ^  D,  of  astigmatism  and  area  of  reversal  of  its  most  my- 
opic meridian  were  27  in.  from  it,  and  its  least  myopic 
meridian  focused  at  one  meter,  the  band  would  be  developed. 
But  a  lower  degree  of  astigmatism  could  not  be  thus  displayed. 

A  low  degree  of  astigmatism  is,  however,  revealed  by  the 
plane  mirror — the  lowest  degree  imaginable.  With  the  plane 
mirror  the  light  may  be  brought  very  close  to  the  mirror — • 
within  2  in.  of  it,  if  necessary.  At  a  working  distance  of  one 
meter,  two  principal  areas  of  reversal  that  are  but  2  in.  apart 
show  very  slight  astigmatism  indeed — the  difference  between 
40/40  and  40/38,  or  the  difference  between  i  D.  and  1.05  D. 
=  .05  D.  As  lenses  are  ground  only  to  .13  D.,  this  is  suf- 
ficient. Since  at  a  distance  of  6  in. — that  is  from  40  to  46  in. — 
it  amounts  to  but  .13  D.,  this  method  conies  very  close  indeed 
to  getting  all  the  astigmatism,  and  does  get  all  that  the  man- 
ufactured trial-case  lenses  will  correct. 

But  it  is  not  necessary,  in  developing  the  banded  appear- 


THE   STUDY    OF   THE   EYE   BY    SKIASCOPY.  1 77 

ance,  to  secure  absolutely  the  maximum  of  diffusion  in  one 
meridian,  and  the  minimum  of  diffusion  in  the  other.  An 
advance  in  that  direction  is  usually  all  that  is  required.  We 
may  get  the  maximum  of  diffusion  more  easily  than  we  can 
get  the  minimum.  If  we  get  the  greatest  diffusion  in  one 
principal  meridian,  and  reduce  diffusion  in  the  other,  we 
usually  develop  the  bands  without  any  trouble.  The  develop- 
ment of  the  banded  appearance  is  quite  a  silent  protest  against 
the  doctrine  of  "indefinite  magnification''  advanced  by  some 
writers.  If  the  image  at  area  3  is  indefinitely  magnified  in  one 
meridian,  what  is  going  to  be  done  with  the  points  in  a  line 
crossing  this  band  at  right  angles? 

The  position  and  direction  of  a  band  of  light  in  the  pupil 
shows  the  position  of  one  of  the  principal  meridians — the 
meridian  in  which  motion  is  neutralized  and  diffusion  is  at  the 
maximum.  In  regular  astigmatism  the  other  principal  merid- 
ian is  at  right  angles  to  it.  But  the  band  and  the  direction 
of  the  band  does  not  show  the  amount  or  degree  of  astigma- 
tism. That  may  be  measured  by  a  sphere  or  cylinder.  It 
is  usually  measured  by  a  cylinder,  for  that  does  not  affect  the 
other  principal  meridian.  The  cylinder  which  increases  dif- 
fusion in  the  second  principal  meridian — the  meridian  at  right 
angles  to  the  band  of  light  if  developed — and  eliminates  mo- 
tion of  the  band  laterally,  measures  the  astigmatism.  With 
the  development  of  diffusion  laterally,  the  band  of  light — if 
developed — of  course  disappears,  along  with  the  disappear- 
ance of  the  clearly  marked  reflex.  The  neutralization  of  mo- 
tion in  one  principal  meridian  eliminates  the  warp  of  the 
reflex;  the  neutralization  of  motion  in  the  other  principal 
meridian  eliminates  its  woof,  and  there  is  nothing  left. 

CORRECTING   ASTIGMATISM. 

The  kind  of  a  cylinder  required  to  correct  astigmatism — 
whether  positive  or  negative — is  shown  by  motion  of  the 
reflex  in  the  meridian  to  be  corrected,  whether  the  banded 
appearance  is  developed  or  not.  If  motion  is  with  the  plane 
mirror  a  plus  cylinder,  axis  at  right  angles  to  the  meridian 
displaying  such  motion,  or  in  or  along  the  band  of  light,  if 
developed,  is  necessary.     If  the  band  of  light  is  vertical,  or 


178  THE  STUDY   OF  THE   EYE   BY   SKIASCOPY. 

there  is  an  elongation  of  the  image  or  reflex  in  the  vertical, 
the  axis  of  the  neutrahzing  positive  cylinder  should  be  ver- 
tical, for  it  is  designed  to  neutralize  or  equalize  motion  in  the 
meridian  of  least  diffusion,  but  slowest  motion — the  horizon- 
tal. But  if  motion  is  against  the  plane  mirror;  or  the  band, 
when  developed,  moves  against  the  plane  mirror  laterally  a 
minus  cylinder  is  required.  With  a  plane  mirror  it  is  evident 
that,  with  motion  against  the  mirror  in  one  meridian,  there 
would  be  no  distinct  banded  appearance,  for  the  least  myopic 
meridian  would  be  neutralized  and  the  observing  eye  be  at 
its  area  of  reversal.  This  would  give  too  much  diffusion  in 
the  second  meridian  to  develop  the  banded  appearance.  But 
a  concave  mirror,  used  in  this  case,  would  show  motion  with 
the  mirror. 

The  power  of  the  cylinder  required  to  neutralize  motion 
in  all  meridians  would  be  determined  by  trial,  the  same  as  the 
power  of  spherical  lenses.  The  only  difiference  is  that  one 
meridian  is  wholly  neutralized  and  all  the  intermediate 
meridians  are  partially  neutralized.  The  cylinder  is  selected 
with  reference  to  its  neutralizing  effect  upon  the  other  prin- 
cipal meridian,  but  it  really  neutralizes  or  completes  the  neu- 
tralization of  the  intermediate  meridians,  at  the  same  time. 

In  the  use  of  the  concave  mirror  to  develop  the  banded 
appearance  in  high  degrees  of  astigmatism,  the  mirror  is  used 
at  such  a  distance  from  the  light  or  luminous  area  as  to  have 
an  area  of  reversal  between  it  and  the  observed  eye,  and  not  as 
described  in  the  last  chapter — eight  inches  from  the  luminous 
area.  The  concave  mirror  is  not  reliable  by  that  plan  in  astig- 
matism, for  the  necessary  inclination  of  the  mirror  to  reflect 
the  pencils  of  light  to  the  observed  eye  develops  a  cylindrical 
efYect  and  gives  an  astigmatic  appearance  when  no  astigma- 
tism is  present.  It  is  useful  only  in  developing  the  banded  ap- 
pearance in  high  degrees  of  astigmatism,  and  to  avoid  working 
at  too  near  a  point  with  the  plane  mirror  in  such  cases  for 
that  purpose.  It  may  also  be  said  of  the  banded  appearance 
that  it  serves  the  purpose  only  of  showing  the  position  of  one, 
and  therefore  of  both,  principal  meridians  in  regular  astigma- 
tism. It  isn't  necessar}-  to  maintain  it  through  an  examination. 
A  spherical  lens,  which  would  destroy  it,  may  be  used  to  neu- 


THE   STUDY   OF  THE   EYE   BY   SKIASCOPY.  I79 

tralize  the  other  meridian,  and  the  correction  of  the  astigma- 
tism be  made  by  correcting  the  elongation  of  the  reflex.  The 
work  can  be  done  more  accurately,  however,  by  bringing  the 
area  of  reversal  for  each  principal  meridian  to  the  fixed  plane 
of  reversal  of  the  observing  eye.  But  even  that  is  not  neces- 
sary to  be  done  for  both  meridians,  for  one  reveals  the  other. 

TEST  OF  ABERRATION. 

Aberration,  as  we  have  heretofore  indicated,  is  more 
clearly  manifest  at  a  point  of  observation  within  one  meter — • 
say  at  I  or  :|  meter — from  the  observed  eye.  In  this  position 
of  the  observing  eye  an  area  of  reversal  for  one  of  the  principal 
meridians  is  brought  to  the  observing  eye,  the  same  as  when 
working  at  one  meter,  to  get  the  efifects  of  maximum  of  dif- 
fusion and  neutralization  of  motion  in  such  meridian.  The 
aberration  test  is  a  static  rather  than  dynamic  test.  The  zonu- 
lar appearance  shown  in  symmetrical  ametropia  is  modified 
somewhat  in  astigmatism,  for  there  is  the  maximaim  of  dif- 
fusion in  but  one  meridian.  The  reflex,  even  in  the  meridian 
of  maximum  diffusion  does  not  extend  entirely  across  the  pu- 
pil, as  shown  at  one  meter,  but  is  confined  to  a  central  area  as 
shown  in  Figs.  57  and  58.  To  neutralize  these  appear- 
ances the  cylinder  is  used  that  gives  the  central  reflex  a 
symmetrical  or  circular  form  corresponding  to  the  luminous 
area.  Such  cylinder  not  only  produces  symmetry  in  the  figure 
upon  area  3  by  modifying  the  incident  pencils,  but  symmetry 
at  area  4  by  modifying  the  emergent  pencils.  It  is  a  very  close 
test,  practically  neutralizing  the  faintest  grain  of  astigmatism. 
Attention  is  directed  to  the  central  area  of  light  alone,  which  is 
very  evanescent  and  disappears  at  the  least  provocation.  To 
work  to  the  best  advantage  a  very  small  luminous  area  is  re- 
quired— the  smallest  that  may  be  made  with  an  iris  diaphragm. 
It  is  not  the  central  area  of  light,  if  there  is  such  an  area,  that 
focuses  at  the  fixed  plane  of  reversal  of  the  observing  eye,  but 
the  darker  area  around  it,  but  by  making  the  central  area  of 
light  symmetrical  the  darker  subcentral  area  is  made  symmetri- 
cal also.  The  figure  will  then  show  slight  lateral  motion — slight 
in  extent  but  not  in  rapidity.  Its  motion  is  quick  but  its  field 
of  motion  is  small.  Neither  the  central  nor  marginal  area  of 
12 


l8o  THE   STUDY   OF  THE   EYE   BY   SKIASCOPY. 

light  can  be  made  to  cross  the  pupil  by  tilting  the  mirror. 
Even  if  the  luminous  area  is  made  larger  the  dark  area  is  not 
eliminated,  nor  are  the  areas  of  light  nicreased  in  extent,  but 
it  requires  but  slight  change  in  the  distance  between  the  ob- 
served and  observing  eye  to  develop  the  reflex  in  all  areas  of 
the  pupil,  because  no  area  of  reversal  is  at  the  fixed  plane ;  and 
but  slight  unsteadiness  of  the  mirror  to  cause  the  reflex  to  dis- 
appear, because  the  area  of  reversal  or  image  anterior  to  the 
observed  eye  has  passed  from  before  the  perforation  in  the  mir- 
ror so  that  the  emergent  pencils  do  not  reach  the  observing 
eye.  The  purpose  of  the  small  luminous  area  is  to  make  the 
image  at  area  3  small,  and  the  image  anterior  to  the  observed 
eye  therefore  small,  so  that  there  will  be  little  unused  light, 
and  the  real  image  anterior  to  the  observed  eye.  may  be  en- 
compassed by  a  small  area  surrounding  the  perforation  in  the 
mirror.  It  requires,  of  course,  but  the  slightest  deflection  to 
take  such  image  from  before  the  perforation,  because,  relative 
to  the  motion  at  area  3,  its  motion  is  very  quick. 

Aberration,  whether  positive  or  negative,  is  not  to  be 
counted  as  an  abnormal  phenomenon,  nor  is  it  the  least  analo- 
gous to  irregular  astigmatism.  It  is,  in  some  respects,  anal- 
ogous to  regular  astigmatism ;  but  is  quite  different  from  that. 
Astigmatism  is  a  variation  of  the  refraction  of  different  merid- 
ians, but  aberration  is  a  variation  of  the  refraction  of  each  me- 
ridian on  accoimt  of  the  variation  in  time  of  the  application 
of  resistance  to  the  waves  of  light  composing  a  pencil.  The 
zonular  appearance  is  due  to  the  fact  that  the  zones  are  alike 
in  time  of  applying  resistance  to  the  waves,  and  waves  have, 
in  each  zone  practically  the  same  degreee  of  curvature.  Of 
course  they  vary  from  point  to  point,  but  vision,  or  visual 
acuity,  is  not  fine  enough  to  distinguish  any  but  the  more  gen- 
eral dififerences.  The  form  of  the  dioptric  surfaces  of  the  eye 
and  the  variations  in  their  indices  of  refraction  are  such 
as  to  minimize  aberration  for  the  ordinary  visual  distances 
— that  is,  between  the  punctum  proximum  and  punctum 
remotum,  for  in  dynamic  as  in  static  refraction  aberration  is 
very  slight.  But  near  the  inner  limit  of  these  distances — that 
is,  near  the  punctum  proximum — aberration  appears.  An  en- 
larged or  dilated  pupil  displays  greater  aberration,  because  a 


THE  STUDY   OF  THE   EYE   BY   SKIASCOPY.  l8l 

larger  area  of  the  dioptric  surfaces  act,  and  by  nearness  the 
action  of  a  larger  area  of  the  lens  is  revealed.  But  with  cor- 
recting glasses  before  the  observed  eye  aberration  of  the  glass 
is  the  chief  element  of  aberration  displayed  in  skiascopy. 

IRREGULAR  ASTIGMATISM. 

Unless  astigmatism  be  such  that  one  cylindrical  surface 
in  connection  with  such  spherical  surface  as  may  be  re- 
quired neutralizes  motion  in  all  meridians  the  astigmatism  is 
irregular.  If  cross  cylinders  at  right  angles  to  each  other  cor- 
rect or  neutralize  all  meridians  there  is  either  an  intermediate 
emmetropic  meridian  or  an  intermediate  meridan  that  a  spher- 
ical lens  will  neutralize.  But  cross  cylinders  not  at  right  angles 
to  each  other  are  reducible,  as  we  have  seen,  to  one  spherical 
and  one  cylindrical  surface.  If  cross  cylinders  such  as  the 
above  neutralize  all  meridians  there  may  be  found  a  sphere- 
cylinder  which  will  have  precisely  the  same  dioptry  in  all  me- 
ridians as  the  compound.  As  far  as  the  spherical  part  of  any 
compound  is  concerned,  that  has  no  effect  upon  the  astigmatic 
element.  It  simply  increases  or  decreases  the  myopia  or  hy- 
peropia, as  the  case  may  be,  leaving  the  astigmatic  element  as 
before. 

There  are  cases,  however,  in  which  the  refraction  is  so 
different  for  different  areas  of  the  pupil  that  neither  sphericals, 
cylindricals  or  compounds  will  neutralize  motion  in  all  merid- 
ians or  at  all  areas  of  the  pupil.  The  conical  cornea  is  an  ex- 
ample of  this  kind.  In  a  skiascopic  examination  the  conical 
cornea  shows  a  triangular  reflex  with  its  apex  at  the  center  of 
the  cornea.  A  glass  could  be  ground  to  neutralize  such  a  con- 
dition, but  unless  the  two  apices — that  of  the  cornea  and  glass 
— coincided  in  position  on  the  visual  axis,  it  would  derange 
vision  more  than  ever.  The  visual  axis  of  the  eye  would  have 
to  pass  directly  through  the  center  of  the  glass  corresponding 
to  the  apex  of  the  conical  cornea,  since  it  must  pass  through 
that  apex  of  the  cornea  itself. 

There  are  often  cases  of  irregular  astigmatism — that  is, 
irregular  refraction  for  different  areas  of  the  pupil  whether 
they  may  be  called  astigmatism  or  not — that  may  be  assisted 
bv  glasses.    It  is  usual  in  such  cases  to  select  from  the  areas 


l82  THE  STUDY   OF  THE   EVE   BY   SKIASCOPY. 

showing  different  power  an  area  most  favorably  located — near- 
est the  central  pupillary  area — and  give  a  correction  for  that 
area.  The  area  of  the  pupil  directly  in  front  of  the  macula 
may  thus  be  made  correct,  even  though  other  pupillary  areas 
are  incorrect  and  tend  to  develop  diplopia. 

But  cases  of  astigmatism  so  irregular  as  not  to  come 
within  any  rule  are  found,  and  there  are  also  pathological  cases 
and  cases  that  have  been  produced  by  surgical  operations  or 
by  accident.  Tliese  are  beyond  the  scope  of  a  work  of  this 
kind,  however  interesting  they  may  be.  Tliey  are  not  cases 
that  the  optician  would  venture  to  deal  with,  although  as  far 
as  refraction  work  may  help  them,  he  is  at  liberty  to  do  what 
he  can. 


CHAPTER  IX. 


CONDITIONS   FAVORABLE  TO   SUCCESSFUL  WORK  IN   SKIASCOPY. 

THE    OPERATING    ROOM    AND    ITS    ARRANGEMENTS. 

PRACTICAL     OPERATING     SUGGESTIONS     TO 

BEGINNERS. 


T  T  is  surprising  what  accurate  results  can  be  obtained  in  ski- 
■'^  ascopy  under  the  least  favorable  conditions.  It  is  a 
method  in  which  the  skill  of  the  operator  counts  for  more  than 
by  any  other  method,  for  it  permits  the  utmost  nicety  of  work. 
But  nevertheless  there  is  no  reason  why  the  operator  should 
not  be  provided  with  every  means  to  make  his  work  the  most 
successful.  While  every  facility  will  not  make  a  good  opera- 
tor of  one  who  does  his  work  carelessly,  a  careful  worker  is 
very  much  aided  by  desirable  arrangements. 

Some  of  the  most  skilled  skiascopists  work  with  an  open 
light,  using  no  skiascopic  chimney  because  they  fail  to  derive 
any  advantage  from  it.  Some  prefer  to  work  with  the  concave 
mirror  altogether.  Some  prefer  large  mirrors  and  others  pre- 
fer small  ones,  as  some  prefer  to  work  at  two  meters,  others  at 
six  meters,  others  at  one  or  one-half  meter.  It  is  a  method 
permitting  such  choice.  But  the  one  meter  distance,  the  plane 
mirror  and  the  skiascopic  chimney  to  limit  the  area  of  light, 
are  more  generally  acceptable. 

THE  OPERATING  ROOM. 

Tlie  best  sort  of  a  dark  room  for  the  practice  of  skiascopy 
is  the  room  in  which  regular  work  is  done — the  regular  operat- 
ing room.  There  are  two  ways  of  making  the  operating  room 
fill  every  requirement  of  the  optician,  both  for  subjective  test- 
ing and  for  the  practice  of  skiascopy  or  other  objective  method. 
One  is  to  have  a  nice  light  room  with  facilities  for  darkening 
it  for  objective  testing;  the  other  is  to  have  a  nice  dark  room 

183 


184  SUCCESSFUL   WORK    IN    SKIASCOPY. 

with  facilities  for  lighting  it.  Of  the  two  the  latter  possesses 
obvious  advantages.  A  room  well  lighted  naturally — that  is 
by  daylight — must  have  window  spaces,  and  to  screen  these  for 
dark-room  work  requires  a  good  deal  of  curtaining  and  a  good 
deal  of  attention.  Even  then,  on  bright  days,  it  is  difficult  to 
darken  the  room  sufficiently.  The  variations  in  light  by  the 
hour  of  the  day  or  position  of  the  sun,  and  variations  due  to 
the  weather,  make  such  a  room  unsatisfactory,  even  for  subjec- 
tive testing.  But  a  naturally  dark  room  lighted  artificially  is 
easily  changed  from  one  to  the  other,  and  the  light,  when  it  is 
lighted,  is  uniform. 

Fig.  59. 


C^craitn-^     l^aam,-    ^CruT.      ?l«.f>-. 


1.  Operator's  Chair.  4.    Trial  Case. 

2.  Patient's  Cliair.  5.    Test  Cards— 20  ft. 

3.  Skiasopic  Light.  6.    Light  at  Test  Cards. 

7.    General  Lights— Ceiling. 

To  control  the  light  in  the  room  the  optician  should  not 
be  compelled  to  pass  around  from  lamp  to  lamp  to  turn  off  or 
turn  on  the  light,  if  that  can  be  avoided.  He  should  be  able  to 
turn  the  light  on  or  off  without  leaving  his  chair  or  his  patient. 
This  may  be  easily  managed  with  incandescent  electric  light- 
ing by  having  the  switch  that  turns  the  light  on  or  ofif  within 
reach  of  the  hand.  There  should  be  three  sets  of  lights:  (i) 
light  overhead  for  the  room  in  general;  (2)  light  near  the  sub- 
jective test  cards,  and  (3)  light  in  the-  skiascopic  chimney.     It 


SUCCESSFUL   WORK    IN    SKIASCOPY,  185 

should  be  so  arrang-ed  that  these  Hghts  may  be  turned  on  or  off 
separately. 

DIMENSIONS  AND  ORDER. 

The  room  should  be  about  20  leet  long  and  of  sufficient 
width  to  contain  all  furnishings — optical  or  otherwise — with- 
out crowding.  The  skiascopic  light  should  be  upon  a  bracket, 
allowing  the  operator  to  move  it  nearer  or  farther,  or  to  elevate 
or  lower  it.  It  will  not  be  found  necessary  to  move  the  lig"ht  to 
opposite  sides  of  the  patient's  head  or  change  his  line  of  vision 
for  examining  the  different  eyes,  nor  for  the  optician  to  change 
his  position.  The  patient  might  be  directed  to  look  to  the  right 
and  left  of  the  mirror,  so  as  to  bring  the  visual  axes  to  the  left 
of  the  operator  when  the  left  eye  is  being  examined,  and  to  the 
right  when  the  right  eye  is  being  examined,  but  even  that  is 
unnecessary,  although  by  having  the  patient  look  in  a  fixed 
direction  to  the  operator's  right  the  reflex  will  be  principally 
to  the  nasal  side  of  the  macula  when  the  right  eye  is  being 
examined,  and  to  the  temporal  side  of  the  macula  when  the  left 
eye  is  being  examined.  The  trial  case  of  lenses  should  be  upon 
a  stand  in  front,  but  to  one  side  of  the  optician,  enabling  him 
to  change  the  lenses  with  as  little  inconvenience  to  himself  as 
possible.  The  accompanying  drawing  will  indicate  the  relative 
positions  of  the  optician  and  his  patient,  the  position  of  the  ski- 
ascopic light,  trial  case,  test  cards,  etc.,  as  well  as  the  general 
arrangements  of  the  room. 

PRACTICAL  OPERATING. 

Before  taking  the  first  skiascopic  view  of  either  eye  vision 
should  be  tested  in  the  ordinary  way  upon  the  test  cards  for 
both  eyes  at  the  20  feet.  If  vision  is  less  than  normal  actual 
vision  should  be  noted  as  B.  E.  20/40,  or  whatever  it  may  be. 
A  H-  I  D.  lens  should  then  be  inserted  in  the  rear  cell  for  each 
eye,  of  the  trial  frames,  and  the  frames  adjusted  comfortably 
upon  the  patient.  General  light  in  the  room  may  then  be 
turned  off,  and  the  patient  be  directed  to  look  at  the  test  cards 
20  feet  away.  The  Hght  should  then  be  turned  off  from  the 
test  cards  and  turned  on  in  the  skiascopic  chimney.  A  little 
time  should  be  allowed  for  the  pupils  to  dilate  and  the  muscles 
of  convergence  and  accommodation  to  relax,  even  more  than 


l86  SUCCESSFUL   WORK    IN    SKIASCOPY, 

they  would  be  relaxed  for  viewing  the  test  cards,  under  the  in- 
fluence of  the  darkened  room  and  the  dimly-seen  objects  in  it. 
Tlie  patient  need  not  hold  the  eyes  in  a  fixed  position  during 
all  this  time — really  the  actual  time  is  very  short — but  he  must 
be  made  to  "look  into  distance"  when  the  optician  begins  to 
work,  slightly  to  the  right  (the  optician's  right)  of  the  mirror. 
This  brings  both  visual  axes  near  to  the  mirror  and  near  to 
the  visual  axis  of  the  observing  eye,  and  gives  a  view,  in  the 
right  eye,  of  an  area  of  the  retina  slightly  to  the  nasal  side,  but 
upon  the  area  of  the  macula. 

As  the  light  from  the  mirror  is  cast  upon  the  face  around 
the  observed  eye  and  made  to  cross  it  in  any  meridian  by  the 
tilting  of  the  mirror,  some  form  of  skiascopic  phenomenon  will 
appear  in  the  pupil  and  show  at  once  whether  the  eye  is  emme- 
tropic, myopic  or  h3'peropic.  If  the  eye  is  emmetropic  the  + 
I  D.  lens  before  it  will  bring  the  area  of  reversal  to  the  observ- 
ing eye — case  2 — or  the  position  in  which  the  motion  of  the 
reflex  cannot  be  determined.  Hence,  if  motion  is  distinctly 
with  the  plane  mirror,  the  eye  under  examination  is  hyperopic, 
and  the  plus  lens  that  neutralizes  motion  or  brings  the  area  of 
reversal  to  the  fixed  plane,  practically  the  cornea,  of  the  ob- 
serving eye,  is  the  full  correction  of  such  hyperopia.  If  mo- 
tion is  against  the  plane  mirror  the  eye  is  myopic,  and  the 
minus  lens  that  neutralizes  motion  at  one  meter  is  the  full  cor- 
rection of  such  myopia.  We  may  not  be  able  to  distinguish 
exactly  the  absolute  point  at  which  reversal  occurs,  but  if  ^  of 
a  diopter  either  way  produces  opposite  motions  the  point  mid- 
way between  them  is  as  close  as  we  can  come  to  it.  If  the 
lens  that  neutralizes  motion  in  one  meridian  does  not  eliminate 
motion  in  all  meridians  astigmatism  is  shown.  The  uncor- 
rected or  unneutralized  meridian  may  be  measured  either  by 
the  sphere  that  corrects  that  meridian,  although  producing 
motion  in  the  meridian  first  neutralized;  or  by  the  cylinder,  axis 
at  right  angles  to  the  unneutralized  meridian,  which  neu- 
tralizes motion  in  the  uncorrected  meridian.  Each  eye  is 
tested  separately  and  its  correction  found. 

The  operator  does  not  require,  if  working  at  one  meter, 
to  be  an  exact  meter  from  the  eye  under  observation.  If  he  is 
6  in.  nearer,  or  34  instead  of  40  in.,  it  makes  a  difference  of  but 


SUCCESSFUL   WORK   IN    SKIASCOPY.  187 

J  of  a  diopter  and  for  two  or  three  inches  the  amount  would 
not  be  worth  noticing.  A  distance  of  6  in.  more  than  a  meter 
would  make  even  less  difference.  The  trial  case  does  not  con- 
tain lenses  graded  fine  enough  to  measure  these  low  degrees. 
But  in  working  at  a  distance  of  less  than  one  meter,  every  inch 
counts  more  and  more  the  nearer  the  working  distance;  but  at 
a  greater  distance,  as  at  two  meters,  inches  cut  very  little 
figure.  If  no  astigmatic  signs  appear,  to  get  the  exact  correc- 
tion of  an  eye  by  skiascopy  requires  a  wonderfully  short  space 
of  time.  The  direction  of  motion  tells  what  kind  of  a  lens  is 
wanted;  the  rapidity  of  motion  and  the  size  of  the  reflex  tells 
about  what  strength  of  lens  is  required.  To  get  that  lens  from 
the  trial  case  that  most  nearly  neutralizes  motion  and  produces 
the  maximum  of  diffusion,  if  not  at  an  exact  meter,  at  an  inch 
or  two  in  front  or  back  of  the  meter  point,  is  but  the  work  of  a 
minute  or  two.  The  operator  may  allow  himself  a  range  of 
six  inches,  three  inches  to  each  side  of  the  meter  point,  to  get 
the  exact  point  of  reversal,  which  none  of  the  trial  lenses  will 
give  him  at  exactly  one  meter;  for  three  inches  to  either  side 
of  the  meter  point,  reduced  to  diopters,  is  absolutely  insignifi- 
cant. No  trial  case  lens  will  measure  it,  for  it  is  less  than  1/12 
of  a  diopter. 

MOVING  THE-  LIGHT. 

The  facilities  for  moving  the  skiascopic  light  are  of  advan- 
tage in  two  ways:  (i)  the  light,  the  observed  eye  and  the  ob- 
serving eye  should  be  in  the  same  horizontal  plane,  and  as 
patients  will  have  considerable  difference  of  body  length  or 
height  of  the  eyes  when  seated  in  a  chair,  the  skiascopic  light 
should  be  adjustable  in  height;  but  (2)  moving  the  light  is  of 
chief  importance  in  bringing  out  the  banded  appearance  in  as- 
tigmatism, and  this  is  effected  by  the  adjustment  of  the  dis- 
tance of  the  light  from  the  mirror.  To  make  these  changes  in 
position,  without  changing  the  general  direction  of  the  beam  of 
light  from  the  skiascopic  chimney,  the  latter  should  rest  upon 
a  rotary  foundation,  so  that  as  the  light  is  moved  forward  or 
backward  upon  the  bracket  or  bracket  hinges  the  chimney  may 
be  rotated  in  the  opposite  direction  from  the  rotation  of  the 
bracket. 

With  the  plane  mirror,  when  the  area  of  reversal  of  the 


loS  SUCCESSFUL    WORK    IN    SKIASCOPY. 

most  myopic  meridian  of  the  observed  eye  is  at  the  observing 
eye,  the  area  of  reversal  of  the  least  myopic  meridian  is  posterior 
to  the  observing  eye.  If  the  observed  eye  has  nearly,  or  quite, 
or  more,  than  one  diopter  of  astigmatism  the  light  cannot  be 
moved  to  the  distance  required  for  the  fullest  display  of  the 
banded  appearance,  for  with  ^  D.  of  astigmatism  it  would  re- 
quire to  be  ^  meter  from  the  mirror,  and  for  ^  D.  of  astigma- 
tism it  would  require  to  be  at  i  meter  from  the  mirror.  That 
is,  if  the  most  myopic  meridian  is  +  (  ~  -|-  i  )  D.  and  the 
least  myopic  meridian  is  +  (  -  +  f  )  D.,  there  is  -J  D.  of 
astigmatism.  To  place  the  light  at  the  same  distance  as  the 
area  of  reversal  of  the  least  myopic  meridian  it  would  require 
to  be  i/f  =  2)/2  meters  from  the  observed  eye,  or  ^  meter  from 
the  mirror.  But  with  ^  D.  of  myopia  the  light  would  require 
to  be  1/^  =  2  meters  from  the  observed  eye  or  i  meter  from 
the  mirror.  It  is  evident  that  with  one  full  diopter  of  astig- 
matism and  the  area  of  reversal  of  the  most  myopic  meridian 
at  the  obsenang  eye,  the  area  of  reversal  of  the  least  myopic  me- 
ridian (which  would  be  emmetropic)  would  be  at  infinity,  and 
the  light  could  not  be  moved  to  infinity.  Hence  the  necessity  of 
using  the  concave  mirror  to  develop  the  most  striking  ap- 
pearance of  the  band  if  the  eye  is  more  than  one  diopter 
astigmatic. 

With  the  concave  mirror  the  least  myopic  meridian,  or 
area  of  reversal  of  the  least  myopic  meridian,  is  brought  to  the 
observing  eye.  Then  the  area  of  reversal  of  the  most  myopic 
meridian  is  somewhere  between  the  observed  and  observing 
eye.  It  is  only  necessary  to  make  the  focal  area  of  the  concave 
mirror  and  the  area  of  reversal  of  this  most  myopic  meridian 
of  the  observed  eye  to  coincide,  or  be  equally  distant  from  the 
mirror,  and  therefore  equally  distant  from  the  observed  eye, 
to  develop  the  banded  appearance  most  strikingly.  This  is 
done,  with  a  concave  mirror  of  given  power,  as  a  25  centi- 
meter mirror,  by  moving  the  light.  The  position  iL  is  neces- 
sary to  place  the  light  indicates  the  position  of  the  area  of  re- 
versal. For  instance,  if  with  the  anterior  area  of  reversal  at  the 
observing  eye,  and  with  a  25  cm.  (+  4  D.)  mirror  the  banded 
appearance  is  developed  most  strikingly  when  the  light  is  20 
in.  from  the  mirror,  the  focal  area  of  the  mirror  is  20  in.  in 


SUCCESSFUL   WORK    IN    SKIASCOPY.  189 

front  of  the  mirror.  Hence  the  other  area  of  reversal  is  20  in.  in 
front  of  the  mirror,  or  20  in.  from  the  observed  eye,  and  it  ha.s 
2  D.  of  myopia  in  that  meridian.  But  if  the  light  requires  to 
be  within  16  in.  of  the  mirror  to  develop  the  banded  appear- 
ance most  strikingly,  2^  D.  of  its  4  D.  power  is  used  in  neu- 
tralizing the  pencils,  leaving  but  i^  D.  to  focus  them.  This 
places  the  focal  area  of  the  mirror  40/1^  =  27  in.  in  front  of 
the  mirror  or  13  in.  from  the  observed  eye.  Hence  that  is  the 
position  of  the  area  of  reversal  of  the  most  myopic  meridian, 
and  3  D.  of  myopia  is  shown  in  that  meridian.  The  amount  of 
astigmatism  in  the  former  case  is  i  D.,  in  the  latter  2  D. 
Again,  if  the  light  has  to  be  14^  in.  from  the  mirror,  2|  D.  of 
its  power  is  used  to  neutralize  the  pencils,  leaving  i^  D.  to 
focus  the  pencils  with  at  40/1 5  =  32  in.,  or  8  in.  anterior  to  the 
observed  eye.  This  shows  5  D.  of  myopia  in  the  most  myopic 
meridian,  or  4  D.  of  astigmatism.  The  nearer  the  light  is 
brought  to  the  mirror  to  develop  the  banded  appearance,  with 
a  concave  mirror,  the  higher  the  degree  of  astigmatism.  But 
the  nearer  the  light,  with  a  plane  mirror,  the  lower  the  degree 
of  astigmatism. 

But,  as  we  have  said  heretofore,  it  is  not  necessary  that 
the  light  be  at  one  area  of  reversal  and  the  observing  eye  at  the 
other  to  develop  the  banded  appearance.  If  the  light  is  some- 
what near  the  other  area  of  reversal,  sufficiently  near  it  to 
make  the  difference  of  diffusion  in  the  two  meridians  striking, 
the  banded  appearance  is  developed.  This  accounts  for  the 
great  differences  noted  in  the  banded  appearance  in  different 
eyes.  In  some  the  band  is  distinct  but  diffusion  spreads  it 
entirely  across  the  pupil  even  in  the  meridian  of  least  diffusion. 
We  do  not  ascertain  the  position  of  the  other  area  of  reversal  by 
calculation,  as  indicated  above,  but  measure  it  by  the  lens 
needed  to  neutralize  motion  in  the  meridian  of  least  diffusion 
The  calculation  is  given  merely  to  show  the  mathematical  basis 
•of  the  bands.  With  a  concave  mirror  of  4  D.  power  (25  centi- 
meter focus)  the  light  cannot  be  brought  to  within  13  in.  of 
the  mirror,  for  at  13  in,  3  D.  of  its  power  would  be  required  to 
neutralize  the  pencils  of  light,  leaving  i  D.  to  focus  them,  and 
that  would  place  the  focal  area  of  the  mirror  one  meter  away, 
or  at  the  cornea  of  the  observed  eye.    No  eye  is  so  myopic  in 


190  SUCCESSFUL   WORK    IN    SKIASCOPY. 

any  meridian  as  to  have  an  area  of  reversal,  or  focal  area  of 
emergent  pencils,  at  its  cornea.  Even  at  2  in.  from  the  cornea 
it  would  show  20  D.  of  myopia,  and  if  the  other  area  of  rever- 
sal were  at  one  meter,  or  one  diopter  myopic,  the  astigmatic 
element  would  be  19  D.,  a  very  unusual,  if  not  unheard  of, 
amount. 

WATCHING  THE  ACCOMMODATION. 

Without  using  a  mydriatic  the  operator  must  be  watchful 
of  the  observed  eye's  accommodation,  to  see  that  v:  does  not 
come  into  play  and  give  him  erroneous  data.  It  is  the  eye's 
static  refraction  that  is  sought  to  be  determined,  and  the  use  of 
the  accommodation  of  the  observed  eye,  of  course,  conceals 
the  real  static  condition.  For  this  reason,  if  the  use  of  the 
accommodation  is  suspected,  the  patient  should  be  relieved  for 
a  moment  by  turning  the  light  upon  the  distant. test  cards  and 
requiring  him  to  converge  and  accommodate  for  20  feet  or 
more.  The  acts  of  convergence  and  accommodation  are  so 
associated  that  to  do  one  is  usually  to  do  the  other,  and  to  relax 
one  is  to  relax  the  other.  The  only  near  object  the  patient  is 
likely  to  fix  is  the  observer  or  the  virtual  image,  so-called,  in 
the  mirror,  really  to  adapt  themselves  to  the  pencils  from  the 
light  that  are  reflected  by  the  mirror.  With  children,  whose 
accommodation  is  so  very  active,  and  who  cannot  be  easily 
made  to  fix  a  distant  object  when  near  and  brighter  things 
may  be  seen,  this  matter  may  be  somewhat  perplexing.  But 
the  photographer  has  quite  as  hard  a  task  when  they  sit  for 
a  picture.  If  the  use  of  mydriatics  is  ever  excusable  it  is  in  the 
case  of  examining  children's  eyes,  especially  by  skiascopy. 
But  children  under  six  or  eight  are  seldom  examined,  and 
they  are  not  difficult  to  manage  if  the  operator  is  ingenious, 
while  little  folks  of  ten  or  twelve  are  often  quite  as  tractable 
as  older  persons,  and  can  be  made  to  relax  the  accommodation 
and  convergence  with  little  trouble. 

HANDLING  THE  LENSES. 

It  is,  of  course,  necessary  as  the  examination  proceeds  to 
change  the  lenses,  reducing  or  increasing  the  strength  as  occa- 
sion may  demand.  This  should  be  done  without  removing 
the  frames,  by  withdrawing  one  and  inserting  the  other  in  its 


SUCCESSFUL    WORK    IN    SKIASCOPY.  I9I 

place  in  the  cell.  It  may  be  necessary  to  lay  aside  the  mirror 
and  lean  forward  to  make  the  change.  The  patient  should  be 
discommoded  as  little  as  possible,  and  the  optician  or  oculist 
should  be  discommoded  as  little  as  possible,  for  it  interrupts 
his  work.  An  experienced  operator  shows  his  skill  in  the 
quickness  and  finesse  with  which  he  can  do  this  work,  and 
some  operators  are  very  skillful  in  doing  it.  But  a  means  of 
making-  these  changes  quickly,  without  putting  the  mirror 
aside,  would  undoubtedly  be  a  valuable  adjunct  in  practical 
skiascopic  work,  and  there  are  some  devices  for  doing  it 
already  in  the  market  to  meet  the  demand,  though  whether 
they  meet  it  satisfactorily  or  not  you  must  judge.  If  the  re- 
fractive error  is  compound  it  may  require  a  number  of  changes 
before  satisfactory  results  are  obtained.  The  patient  must  not 
be  tired  out  with  a  long  and  tedious  examination,  and  the 
operator  will  find  it  convenient  to  vary  the  distance  and  deter- 
mine about  what  lens  is  required  in  that  way,  rather  than  run 
through  the  whole  category  of  lenses  to  get  at  the  glass  needed. 
He  can,  by  varying  his  distance,  measure,  with  reasonable 
accuracy,  the  lens  strength  needed  to  bring  the  area  of  reversal 
to  the  point  required.  If,  for  instance,  he  finds  by  this  method 
that  the  area  of  reversal  is  -i  meter  from  the  observed  eye,  a 
—  I  D.  will  bring  it  near  the  poijit  required,  and  the  proper 
lens  may  be  inserted  at  once. 

PROVING   RESULTS. 

Both  eyes  are  tested  separately  in  the  same  way.  Skias- 
copy is  a  strictly  monocular  test,  and  the  error  of  each  eye  is 
measured  separately  and  by  itself.  It  will  be  necessary,  when 
the  suitable  correction  for  each  eye  is  found  to  prove  the  result 
and  to  determine  whether  the  eyes  will  bear  the  full  correction 
or  not.  The  proof  of  the  objective  test  is  the  patient's  subjec- 
tive vision  and  visual  comfort.  When  both  glasses  are  in  their 
place  in  the  trial  frame  the  light  should  be  turned  upon  the  dis- 
tant card,  and  the  effects  of  the  glasses  determined.  The 
operator  will  know  to  what  extent  vision  is  improved  for  each 
eye,  and  can  tell  whether  normal  vision  will  result  or  not,  but 
he  does  not  know  whether  the  patient  can  wear  the  glasses — 
the  full  correction — comfortably  or  not.    The  visual  test  on  the 


192  SUCCESSFUL   WORK    IN    SKIASCOPY. 

distant  cards  will  alone  clear  up  this  point.  When  the  light  is 
turned  on  and  the  patient  is  asked  to  report  on  these  mat- 
ters, the  objective  test  is,  of  course,  completed.  If  the  glasses 
do  not  feel  comfortable,  if  they  "hurt"  the  eyes  or  do  not  feel 
''easy"  and  "restful,"  as  well  as  give  good  vision,  there  is  prob- 
ably a  binocular  complication  or  asthenopic  trouble  which  the 
glasses  do  not  relieve,  or  even  make  more  distressing,  or  pro- 
duce where  it  did  not  exist  before.  What  that  trouble  is  can- 
not be  determined  by  skiascopy.  He  must  proceed  from  this 
point  by  other  methods,  but  having  the  full  refractive  error 
for  each  eye  will  be  a  great  help  to  him  in  his  further  work. 
It  is  usually  a  good  plan  to  obscure  one  eye  while  the  vision 
of  the  other  is  subjectively  tested,  so  that  your  patient  will 
understand  the  accuracy  of  your  work  although  the  binocular 
effect  is  unsatisfactory.  He  will  then  appreciate  the  nicety  of 
your  work,  and  be  all  the  more  willing  to  trust  to  you  for  the 
rest.  You  will  gain  his  confidence  at  a  critical  point,  whereas, 
if  both  eyes  were  uncovered  and  he  is  given  to  understand  that 
this  is  the  result  of  your  work,  no  matter  how  carefully  you 
may  have  corrected  each  eye,  if  there  is  a  binocular  complica- 
tion he  will  be  apt  to  think  that  you  have  failed.  Comfortable 
vision  is  preferable  always  to  everything  else,  and  everv-  cor- 
rection of  the  eyes  by  glasses  that  improve  vision  at  the  sacri- 
fice of  comfort  is  a  failure  of  the  worst  kind.  We  cannot  here 
go  into  the  details  of  securing  the  best  vision  with  the  greatest 
comfort,  but  it  will  be  found  necessary  in  all  work  to  pay  the 
strictest  attention  to  it. 

SUGGESTIOXS  TO  BEGINNERS. 

Skiascopy  as  a  method  of  ocular  examination  is  one  that 
grows  accurate  and  reliable  only  with  experience.  Practice 
makes  perfect.  The  beginner  should  become  familiar  with 
effects  by  practice  upon  a  schematic  eye  before  attempting  to 
do  work  with  real  eyes.  The  distinctions  between  cases  i,  2 
and  3  should  be  thoroughly  mastered  both  in  theory  and  prac- 
tice. The  peculiar  effects  of  aberration  should  also  be  carefully 
studied.  The  appearances  under  either  case  i,  2  or  3  are  not 
by  any  means  the  same.  Under  case  i  we  may  have  motion 
with  the  plane  mirror,  but  diffusion  and  rapidity  of  motion 


SUCCESSFUL   WORK    IN    SKIASCOPY.  193 

vary  with  every  approach  toward  or  recession  from  reversal. 
The  same  may  be  said  of  case  3.  But  case  2,  or  the  point  when 
diffusion  reaches  the  maximum  and  motion  is  indeterminate, 
is  the  most  important  phase  of  the  whole  work.  It  is  judged 
by  what  you  don't  see  rather  than  what  you  do  see,  but  when 
a  low  minus  lens  develops  motion  in  one  direction  and  a  low 
plus  lens  develops  motion  in  the  other  direction,  there  can  be 
no  doubt  as  to  the  real  location. 

Beginners  should  work  upon  cases  of  symmetrical  ame- 
tropia first.  That  is  the  schematic  eye  should  be  set  at  an  un- 
known point,  and  with  the  trial  case,  mirror  and  light  the 
amount  of  ametropia  should  be  measured.  The  correctness  of 
the  results  can  then  be  ascertained  by  seeing  how  near  the  ex- 
act result  has  been  determined.  This  work  should  be  done 
over  and  over,  working  at  one  meter.  If  a  lens  brings  the  area 
of  reversal  to  the  eye,  as  shown  by  the  appearances  in  case  2, 
the  accuracy  of  the  result  may  be  tested  without  removing  the 
correcting  lens,  by  advancing  the  mirror  and  observing  eye 
a  few  inches  toward  the  observed  eye  to  develop  case  i,  and 
withdrawing  it  a  few  inches  from  the  one  meter  point  to  de- 
velop case  3.  In  this  way  the  nearness  of  the  area  of  reversal 
to  the  observing  eye,  if  it  is  not  at  it  exactly,  is  discovered.  It 
is  surprising  how  quickly  under  tliis  plan  the  skiascopic  in- 
stinct is  developed.  The  author  has  seen  students  in  three  days' 
work  of  an  hour,  or  even  less,  a  day,  become  very  close  work- 
ers for  all  kinds,  or  rather  degrees,  of  myopia  and  hyperopia. 
The  appearances  of  aberration  are  confusing  at  first  only.  As 
we  have  said,  these  are  not  abnormalities  but  natural  optical 
effects.  If  the  dioptric  surfaces  of  the  eye  were  perfectly  spher- 
ical, and  the  index  of  refraction  for  all  areas  of  the  cornea 
and  the  lens  were  uniform,  spherical  aberration  in  the  eye 
would  be  more  pronounced  than  it  is.  Aberration  in  the  diop- 
tric surfaces  is  reduced  by  the  want  of  absolute  sphericity,  and 
by  variations  in  the  index  of  refraction  in  them.  It  is  not  pro- 
duced by  such  want.  Whether  aberration  is  negative  or  posi- 
tive is  not  a  matter  of  any  optical  importance.  No  eye  is  abso- 
lutely without  aberration,  and  if  one  were,  the  placing  of  a 
glass  lens  before  it  would  develop  aberration  for  the  compound 
system. 


194  SUCCESSFUL   WORK   IN    SKIASCOPY. 

For  experimental  work,  and  especially  for  the  use  of  stu- 
dents, the  author  has  taken  an  ordinary  Thorington  eye,  taken 
the  lens  out  and  had  special  lenses  ground,  one  of  +  20  D.  sph 
3  —  2D.  cyl.,  and  another  of  +  20  D.  sph.  3  —  i  D.  cyl., 
which  have,  with  the  lens  removed,  been  mounted  in  paste- 
board which  may  be  inserted  in  the  eye  so  that  the  lens  is  ex- 
posed at  the  pupil.  By  placing  one  of  the  compound  lenses  in 
place  any  form  of  astigmatism  of  the  schematic  eye  may  be 
produced  by  moving-  the  tube  containing  retinal  area.  To 
measure  and  neutralize  the  myopia  and  hyperopia  and  neutral- 
ize the  astigmatism  gives  the  beginner  real  work  to  do;  for  he 
must  measure  the  amount  and  determine  the  axis  of  the  neu  • 
tralizing  cylinder  as  well  as  find  the  spherical  correction.  As 
the  compounds  contain  the  full  spherical  power  at  one  surface, 
the  optical  center  of  the  lens  is  nearer  the  pupil  or  farther 
from  the  retina  than  with  a  bi-convex  lens,  such  as  is  used 
in  the  regular  eye.  This  makes  the  dioptric  marking  a  little 
out  of  plumb,  but  that  need  not  bother  seriously.  The  object 
in  putting  the  astigmatic  factor  m  the  one  lens  is  merely  to 
conceal  it  so  that  a  student  does  not  know,  except  by  skia- 
scopic  test,  whether  the  spherical  lens  or  one  of  the  com- 
pounds is  in  the  eye;  and  if  he  finds  it  is  compound,  he  doesn't 
know  the  amount  nor  direction  of  the  axis  without  he  deter- 
mines it  by  test. 


CHAPTER  X. 


SKIASCOPIC     DEVICES    AND     INVENTIONS.       INGENIOUS    APPLI- 
ANCES  DEVISED   TO    MAKE   THE   METHOD   MECHANI- 
CALLY   PERFECT    AND    COMFORTABLE    FOR 
THE  OPERATOR. 


A  METHOD  of  ocular  examination  so  simple  in  its  essen- 
tial details,  and  so  exact  in  its  results  when  skillfully 
employed,  is  naturally  very  attractive  to  optical  workers.  It  is 
•chiefly  valued  because  it  is  an  objective  method,  and  successful 
work  by  it  is  prima  facie  evidence  of  unusual  skill.  But  it  is  a 
method  that  must  be  worked  finely,  if  at  all,  and  does  not  per- 
mit of  any  "bull  in  the  china  shop"  disregard  of  its  fine  points. 
Those  who  attempt  to  operate  it  coarsely  usually  fail,  and  then 
they  are  apt  to  condemn  the  method  when  their  failure  is  their 
own  fault.  To  do  fine  work,  however,  the  different  skiascopic 
phenomena  or  appearances  under  cases  i,  2  and  3  must  be 
made  thoroughly  familiar,  so  that  the  operator  will  know  at 
a  glance  about  how  near  the  are^  of  reversal  is  to  his  eye. 
To  make  the  method  more  certain  and  for  the  ease  or  comfort 
of  the  operator  in  using  it  some  ingenious  devices  have  been 
made.  There  are  no  doubt  others  being  devised  every  year, 
some  practical  and  valuable,  but  others  of  very  little  use.  We 
will  consider  a  few  of  the  chief  instruments  of  this  kind. 

It  will  not  be  necessary  to  speak  here  of  the  forms  of  the 
■skiascopic  mirrors  or  of  the  chimneys,  as  they  have  already 
received  all  necessary  attention.  The  direction  of  the  other 
devices  have  been: 

(i)  To  make  the  changes  of  lenses  before  the  observed 
eye  quickly  and  comfortably  without  having  to  lay  aside  the 
mirror. 

(2)  To  definitely  locate  the  axis  of  rotation  of  the  mirror 
in  testing  an  oblique  meridian,  and  therefore  locating  accu- 
rately the  meridian  tested. 

13  195 


196  SKIASCOPIC    DEVICES   AND    INVENTIONS. 

(3)  To  reduce  the  intervals  of  evolutionary  spaces  to  cer- 
tainty as  to  distance. 

(4)  To  make  the  position  of  the  skiascopic  light  readily 
changeable,  as  required  in  the  development  of  the  banded  ap- 
pearance in  astigmatism. 

(5)  To  neutralize  in  whole  or  in  part  the  incident  pencils 
of  light  before  they  reach  the  observed  eye,  so  as  to  sharpen 
the  definition  and  intensify  the  light  or  reflex  at  area  3. 

Some  quite  satisfactory  results  have  been  obtained  in 

these  directions,  as  will  appear  from  the  following  descriptions 

and  illustrations: 

I.  LENS  HOLDERS. 

Commercially  these  are  known  as  skiascopes  lather  than 
the  skiascopic  mirror,  which  is  more  frequently  called  a  "retin- 
oscope"  in  the  West,  although  the  East  seems  to  favor  "skia- 
scope" for  the  mirror,  the  same  as  it  favors  "skiascopy"  rather 
than  "retinoscopy"  for  the  method. 

I.    THE   WURDEMANN    SKIASCOPE. 

Fig.  60  illustrates  an  instrument  devised  by  Dr.  Wurde- 
mann,  of  Alilwaukee.    It  consists  of  batteries  of  plus  and  minus 


lenses  arranged  in  separate  rows  in  an  oblong  frame,  with  a 
handle  for  the  patient  to  grasp  and  hold  in  an  upright  posi- 
tion so  as  to  place  the  lens  desired  before  the  observed  eye. 
The  patient  is  given  the  task  of  holding  the  instrument  as  di- 
rected by  the  operator,  and  changing  the  position  so  as  to  bring 
different  lenses  before  the  eye,  while  the  operator  gives  his 
attention  to  the  skiascopic  appearances  and  to  manipulating 
the  light  and  the  mirror.  This  enables  the  operator  to  devote 
his  entire  attention  to  his  real  work,  and  imposes  but  a  slight 
burden  upon  the  patient.  With  this  and  other  instruments  of 
the  kind  care  must  be  taken  to  avoid  producing  a  cylindrical 


SKIASCOPIC    DEVICES    AND    INVENTIONS. 


197 


effect  by  inclitiing-  the  lens  to  the  visual  axes,  or  a  prismatic 
effect  by  not  having-  the  lens  centered  over  the  observed  eye. 


2.   THE  GENEVA  SKIASCOPE. 


This  instrument  is  different  from  the  Wurdemann  instru- 
ment chiefly  in  having  the  plus  lenses  on  one  standard  and  the 
minus  lenses  on  another,  as  shown  by  the  figure  (Fig.  61).    It 


gives  the  patient  a  lighter  weight  to  hold,  and  the  absence  of 
all  interfering  material  around  the  lenses  makes  it  easier  to  get 
the  close  position  required.  Lightness  is,  of  course,  quite  an 
advantage,  as  it  makes  the  assistance  of  the  patient  as  little 
burdensome  as  possible. 

3.    THE   HARDY   SKIASCOPE. 

The  Hardy  instrument  is  a  further  departure  from  the 
Wurdemann  instrument,  as  shown  by^the  figure  (Fig.  62).    In 


Fiu.  G2. 


it  the  lenses  are  arranged  in  circular  order  in  a  circular  disc, 
which  is  rotated  to  bring  different  lenses  before  the  observed 
eye.    The  patient  holds  the  instrument  in  a  fixed  position  be- 


198 


SKIASCOPIC    DEVICES    AND    INVENTIONS. 


fore  the  observed  eye,  and  brings  the  different  lenses  into  posi- 
tion by  rotating  the  wheel  as  directed  by  the  operator.  The 
same  care  is  required  not  to  tilt  the  lenses  in  this  as  in  the 
other  two  instruments. 

4.    DR.   grain's  device. 

Dr.  C.  H.  Grain,  of  Chicago,  has  devised  a  more  complete 
instrument  than  any  of  the  above,  as  may  be  seen  by  the  illus- 
tration (Fig.  63).    Foundationally  it  resembles  the  Hardy  Ski- 


FlG.  63. 

ascope,  but  has  additional  features.  It  rests  upon  a  standard 
and  is  not  held  in  the  hand.  It  is  elevated  or  lowered  to  suit 
the  position  of  the  eye  to  be  examined  by  means  of  an  attach- 
ment in  the  standard.  It  also  has  a  chin-rest  and  an  opaque 
cover  for  the  eye  not  under  examination,  and  a  bend  in  the 
horizontal  frame-work  to  fit  the  nose  when  the  eye  is  in  place. 
There  is  also  in  front  of  the  disc  containing  the  lenses,  at  the 
point  where  the  observed  eye  is  placed,  a  cell  in  which  to  put 


SKIASCOPIC    DEVICES   AND    INVENTIONS. 


199 


a  trial-case  lens  or  cylinder.  When  the  right  eye  is  examined 
the  patient  is  seated  upon  the  right  of  the  instrument,  and 
vice  versa  for  the  left  eye.  Two  indices  are  so  placed  that 
they  indicate  the  lens  that  is  before  the  observed  eye  to  an 
office-assistant,  who  may  rotate  the  disc  or  wheel  containing 


Pig.  64. 


the  lenses  as  desired.  Cutting  off  the  vision  of  the  eye  not 
under  examination  by  the  opaque  disc  would  interfere  with 
the  easiest  means  of  controlling  the  accommodation — that  is, 
by  the  principle  of  convergence — if  the  eye  were  not  under 
atropine  or  other  mydriatic,  but  as  the  inventor  uses  a  mydri- 
atic in  all  cases  this  principle  is  of  little  importance  to  him. 


200  SKIASCOPIC    DEVICES   AND    INVENTIONS. 

5.    THE  JENNINGS'  SKIASCOPE. 

The  general  appearance  of  this  instrument  is  shown  in 
the  accompanying  figure  (Fig.  64).  It  is  constructed  on  the 
principle  of  the  Morton  ophthalmoscope,  and  different  lenses 
are  brought  before  the  observed  eye  by  means  of  a  long  axle 
reaching  the  operator,  by  which  a  wheel  in  the  lower  part  of 
the  instrument  rotates  the  battery  of  lenses  in  the  upper  part. 
The  operator  can  in  this  manner  bring  any  lens  desired  before 
the  observed  eye  without  changing  his  own  position  or  neg- 
lecting his  work  with  the  mirror,  or  requiring  the  assistance  of 
anyone.  It  seems  to  meet  the  requirements  of  such  an  instru- 
ment better  in  many  respects  than  any  other  "skiascope"  or 
lens  holder.  The  author  has  not  seen  the  instrument,  but  its 
operation  is  simple  to  anyone  acquainted  with  the  Morton 
opthalmoscope,  from  a  study  of  the  illustration. 

There  are  probably  other  instruments  in  this  line,  the  pur- 
pose of  all  being  the  same — that  of  changing  the  lenses  before 
the  observed  eye  quickly  and  at  as  little  inconvenience  to  the 
operator  and  his  patient  as  possible.  They  are  a  convenience 
rather  than  a  necessity. 

2.  MIRROR'S  AXIS  OF  ROTATION. 

*  When  the  mirror  is  tilted  so  as  to  cause  the  area  of  light 
on  the  face  to  pass  across  the  observed  eye,  it  is  of  course 
rotated  slightly  upon  an  axis  corresponding  to  the  position 
of  the  handle.  It  is  comparatively  easy  to  fix  the  vertical 
(90°)  and  horizontal  (180°)  axes  of  rotation,  but  when  the  rota- 
tion or  tilting  of  the  mirror  is  in  an  oblique  axis  a  means  of 
determining  exactly  the  axis  is  important,  for  the  axis  of 
rotation  of  the  mirror  is  at  right  angles  to  the  meridian  of  the 
eye  being  tested,  or  to  motion  of  the  light  on  the  face  A  device 
to  fix  the  axis  of  rotation  of  the  mirror  has  been  invented  by 
Dr.  Charles  Gordon  Fuller,  of  Chicago,  which  is  shown  in  the 
accompanying  figure  (Fig.  65).  An  opaque  disc  containing  a 
small  skiascopic  mirror  is  set  axially  in  a  rim  or  ring  on  which 
are  marked  the  degrees  of  circular  or  angular  measure.  Rota- 
tion of  the  disc  in  the  outer  rim  of  course  changes  the  axis  of 
the  mirror  or  disc  on  which  the  mirror  is  set,  without  changing 


SKIASCOPIC   DEVICES   AND    INVENTIONS. 


201 


the  plane  of  the  mirror,  and  the  degree  marks  on  the  rim  show 
the  position  of  the  axis  for  tilting  the  mirror.  The  outer  rim 
is  attached  to  a  fixed  standard  which  is  vertical  in  position,  but 


Fig.  65. 


it  may  be  held  in  the  hand.  If  the  mirror  is  laid  aside,  as  for 
the  purpose  of  changing  the  lens  before  the  observed  eye,  it 
may  be  picked  up  again,  and  will,  of  course,  have  the  same 
angle  or  axis  of  rotation  as  before.    The  mirror  is  used  in  con- 


202  SKIASCOPIC    DEVICES   AND    INVENTIONS. 

nection  with  a  specially  devised  skiascopic  chimney  containing 
a  long  arm  that  confines  the  pencils  of  light,  and  fixes  the  dis- 
tance. This  is  of  less  value,  we  think,  than  the  principle  above 
described. 

3.  FIXING  THE  INTERVALS. 

There  have  been  invented  quite  a  number  of  devices  to  fix 
absolutely  the  distance  or  spaces  of  the  three  intervals.  Effort 
in  this  matter  seems  to  have  been  misdirected  in  most  cases, 
for  it  fails  to  take  into  account  the  value  of  being  able  to 
change  the  intervals  at  will.  By  this  means  we  may  produce 
nicer  shades  of  skiascopic  effects  than  by  any  other  means. 
Every  change  in  the  position  of  the  observing  eye  has  a  value 
equivalent  to  a  lens  before  the  observed  eye.  Moving  from  a 
distance  of  one  meter  to  a  distance  of  one-half  meter  from  the 
observed  eye  has  a  value  of  but  one  diopter.  Motion  from  one 
meter  to  a  point  an  inch  nearer  the  observed  eye  has  a  value 
of  less  than  .03  of  a  diopter.  A  half-inch  or  quarter-incli  has 
still  less  value.  As  the  observing  eye  may,  under  free  action, 
be  at  any  desired  distance  from  the  observed  eye,  the  varieties 
of  lens-action  such  changes  are  equivalent  to  are  very  numer- 
ous.    Fixing  the  distance  eliminates  all  this. 

There  are  also  accompanying  dynamic  effects  during  the 
change  of  any  of  the  intervals,  and  as  skiascopy  is  essentially 
a  dynamic  test,  fixing  the  distances  of  all  the  evolutionary 
spaces  would  eliminate  such  special  dynamic  features.  It 
would  be  equal  to  the  invention  of  a  ship-builder  who  devised 
a  rudder  by  which  the  ship  would  be  compelled  always  to  sail 
in  one  direction  as  regards  the  wind.  It  is  a  good  deal  better 
to  have  ships  that  are  able  to  sail  in  many  directions,  whatever 
the  wind,  and  a  rudder  capable  of  changing  the  course  as  de- 
sired. Fixing  the  intervals  absolutely  would  therefore  inter- 
fere with  the  operator  in  using  the  method  completely,  for  im- 
portant results  are  obtained  by  varying  the  intervals,  slightly 
or  considerably,  as  in  developing  the  banded  appearance  in 
astigmatism,  or  finding  an  area  of  reversal  that  no  regular  trial 
lens  will  bring  exactly  to  the  right  point.  Of  course,  any  de- 
vice that  fixes  the  length  of  the  intervals  absolutely  makes  the 
result  more  accurate  for  that  fixed  distance,  but  it  also  confines 
the  work  of  the  operator  within  the  same  limits.     He  must 


SKIASCOPIC    DEVICES   AND    INVENTIONS. 


203 


get  all  he  wants  within  these  limitations  or  do  without  it.  It 
will  be  found  better,  w^e  think,  not  to  handicap  skiascopy  in 
this  way.  Better  a  little  uncertainty  as  to  amount  or  quan- 
tity of  error  than  being  fenced  into  a  limited  field  of  operation. 
The  intervals  in  skiascopy  are  evolutionary  spaces.  They  are 
factors  in  the  general  results,  and  it  is  desirable  to  be  able  to 
use  them  as  factors,  which  cannot  be  done  if  they  are  fixed 
absolutely.  That  is,  the  dynamic  efifects  of  changing  the  in- 
tervals is  eliminated  the  moment  the  distances  are  made  fixed. 

4.  POSITION  OF  LIGHT. 

The  facilities  for  changing  the  position  of  the  skiascopic 
light  seem  to  be  met  as  fully  as  possible  by  the  adjustable 


Fig.  67. 


bracket  (Figs.  66  and  6'j').  It  gives  a  variation  in  the  distance 
of  the  light  from  the  mirror  of  nearly  two  meters,  or  from  as 
near  a  point  as  you  wish  it  to  two  meters,  without  changing 


204  SKIASCOPIC    DEVICES   AND    INVENTIONS. 

the  position  of  operator  or  patient.  For  degrees  of  astigma- 
tism of  more  than  one  diopter  it  is  usually  better  to  employ 
the  concave  mirror,  and  control  then  the  position  of  the  imme- 
diate source  of  light,  which  requires  but  slight  variation  in  the 
position  of  the  real  skiascopic  light.  The  banded  appearance 
may,  however,  be  made  sufficiently  distinct  with  a  plane  mirror 
to  show  the  meridians,  even  with  a  higher  degree  of  astigma- 
tism than  one  diopter.  The  adjustable  bracket  is  made  for  all 
kinds  of  lights,  and  is  a  great  convenience,  as  it  can  be  raised 
or  lowered  as  well  as  removed  farther  from  or  brought  nearer 
the  mirror. 

5.  NEUTRALIZING  INCIDENT  PENCILS. 

This  may  be  accomplished  in  either  of  two  ways:  (i)  by 
having  a  neutralizing  or  under-neutralizing  lens  between  the 
light  and  the  mirror,  or  (2)  by  using  a  concave  mirror  with  the 
skiascopic  light  at  or  within  its  principal  focal  distance.  This 
introduces  optical  factors  which  modify  the  waves  on  their 
way  to  the  observed  eye.  An  exactly  neutralizing  lens — that 
is  a  +  16  D.  lens  2^  in.  from  the  light,  and  so  placed  in  interval 
I  as  to  intercept  the  pencils  on  their  way  to  the  mirror,  has  the 
effect,  so  far  as  the  curvature  of  the  waves  is  concerned,  of 
causing  the  luminous  area  to  recede  to  infinity.  But  the  dif- 
ferent pencils,  or  rays  of  the  different  pencils,  have  practically 
the  same  divergence  as  before.  Such  a  lens,  in  its  focal  posi- 
tion, has  its  maximum  of  magnifying  effect  upon  the  luminous 
area,  and  hence  the  luminous  area  may  be  small,  and  should  be 
some  characteristic  figure,  such  as  a  cross  or  triangle,  in  order 
to  be  confined  within  the  central  area  of  the  lens  and  produce 
as  little  aberration  as  possible.  This  would  sharpen  the  defini- 
tion at  area  3,  if  the  observed  eye  is  fully  corrected,  and  pro- 
duce also  a  clear  definition,  without  diffusion,  at  area  4,  A 
lens  of  less  than  full  neutralizing  power  would  tend  in  the 
same  direction,  and  the  evolution  of  the  waves  through  the 
remaining  space  of  interval  i  and  all  of  interval  2  would  tend 
still  further  to  neutralize  them.  But  if  the  lens  or  mirror 
transposed  the  pencils,  the  remaining  portion  of  interval  i  and 
all  of  interval  2  would  tend  to  augment  the  curv^ature  of  the 
waves. 


SKIASCOPIC    DEVICES    AND    INVENTIONS.  205 

In  the  use  of  tubes  in  which  to  confine  the  pencils — or 
shut  out  extraneous  light — we  introduce  mechanical  interfer- 
ence with  the  peripheral  areas  of  all  the  waves,  both  of  the  in- 
cident and  emergent  pencils,  and  set  up  cross  waves  and  reflec- 
tions unless  the  walls  of  the  tube  are  thoroughly  deadened  by 
light-absorbing  materials  or  diaphragms  inserted  to  intercept 
them  and  reflect  them  in  directions  that  will  not  permit  their 
reaching  either  objective  or  subjective  pupil.  Such  dia- 
phragms will  have  no  optical  effect — will  not  modify  the  curva- 
ture of  the  waves  passing  through — but  they  make  a  nice  ad- 
justment of  the  spaces  necessary. 

The  use  of  diaphragms  in  optical  tubings  of  this  kind  has 
been  thought  to  have  a  modifying  effect  upon  the  pencils  of 
light,  but  this  cannot  be  the  case.  It  is  true  that  one  may 
produce  a  very  fair  image  of  the  flame  of  a  candle  through  a 
pin-hole  disc,  but  such  image  is  the  product  of  untransposed 
pencils  of  light  passing  through  the  pm-hole.  The  inversion 
of  the  image  is  due  to  the  natural  inversion  of  the  different 
pencils  which  pass  through  the  same  opening  but  in  different 
directions,  as  explained  under  the  principle  of  inversion.  Chap- 
ter R'.  The  screen  that  receives  or  reacts  upon  these  pencils 
contains  little  classified  areas,  each  of  which  receives  all  the 
light  from  one  minute  pencil,  and  part  of  the  light  from  ad- 
joining pencils.  These  little  areas  correspond  to  diffusion  cir- 
cles when  the  screen  is  held  slightly  beyond  its  focal  position 
for  a  lens,  except  that,  in  the  latter  case,  the  diffusion  circles 
widen  rapidly  with  the  removal  of  the  screen  from  its  focal 
position.  In  the  image  produced  by  a  pin-hole  disc  the  screen 
may  be  varied  in  position  several  inches  without  producing  but 
little  effect  on  the  clearness  of  the  image,  since  it  is  but  slightly 
farther  from  the  center  of  curvature  of  the  waves  than  before; 
while  with  the  focused  pencils  the  removal  of  the  screen  ^  in. 
places  it  just  that  distance  farther  from  the  center  of  curvature. 

THE  PRENTICE  RETINOSCOPE. 

This  is  an  instrument  being  manufactured  by  the  Geneva 
Optical  Co.,  of  Chicago,  that  seems  to  embody  all  the  valuable 
principles  of  a  mechanical  character  embraced  in  other  devices. 
It  has  the  same  principle  of  tilting  the  mirror  in  any  axis  re- 


206 


SKIASCOnC    DEVICES    AND    INVENTIONS. 


quired  as  Dr.  Fuller's  invention;  it  has  a  lens  holder  essenti- 
ally the  same  as  the  Hardy  skiascope;  the  intervals  are  fixed 
by  a  system  of  tubing  that  confines  both  the  incident  and 
emergent  pencils  of  light;  a  plane  or  concave  mirror  is  equally 


available;  a  means  of  inserting  a  disc  giving  any  desired  form 
to  the  luminous  area,  or  a  lens  to  neutralize  or  partly  neutral- 
ize the  incident  pencils,  is  provided  in  the  space  of  the  first  in- 
terval; and  the  tubing  is  lined  with  light-absorbing  surfaces. 


Fig.  G9. 


and  contains  intercepting  diaphragms  to  reduce  the  pencils  of 
light  to  the  dimensions  needed  for  the  purpose  of  preventing 
cross  waves  and  reflections.  Light  may  be  provided  by  an  in- 
candescent gas  film,  electric  light  or  by  an  acetylene  gas  lamp. 


SKIASCOPIC    DEVICES    AND    INVENTIONS. 


207 


Tig.  68  illustrates  a  cross-sectional  view  of  the  instrument, 
and  Fig.  69  its  general  appearance.  It  may  be  modified  in 
some  particulars,  but  the  details  as  shown  will  probably  not 
be  changed  essentially. 

The  observed  and  observing  eyes  are,  when  at  the  respec- 
.tive  eye  cups  of  the  instrument,  20  inches  apart,  and  therefore 


a  +  2  D.  lens  is  necessary  to  neutralize  the  distance  of  the  ob- 
server, or  to  focus  the  emergent  pencils  in  emmetropia  at  his 
eye.  With  the  instrument  the  pupillary  display  is  wonderfully 
distinct,  and  a  dark  room  is  not,  of  course,  required  in  its  oper- 
ation. Its  delicacy  is  shown  by  the  fact  that  the  insertion  of  a 
.13  D.  lens  will  produce  distinct  reversal. 

The  present  instrument  does  not  provide  the  means  for 
bringing  out  the  most  distinct  banded  appearance  in  astigma- 


208  SKTASCOPIC    DEVICES    AND    INVENTIONS. 

tism,  although  with  a  small  opening  before  the  light  and  one 
meridian  neutralized,  the  band  is  plainly  seen.  An  improve- 
ment in  the  incident  tube  by  which  a  movable  lens  of  about 
+  8  D.  could  be  placed  in  any  desired  position  from  8  in. 
to  4  in.  of  the  light  would  give  the  means  of  controlling  the 
position  of  the  light  or  the  source  of  the  incident  pencils  so 
as  to  make  the  bands  the  most  distinct.  Such  improvement 
would,  however,  increase  the  cost  of  the  instrument  as  an 
achromatic  lens  would  be  necessary  for  the  purpose.  The  in- 
strument in  its  present  form  is,  however,  a  very  delicate  test 
for  every  form  of  ametropia. 

The  provision  in  the  instrument  for  controlling  the  ac- 
commodation of  the  eye  under  examination  is  an  eye  clip  con- 
taining a  cell  for  the  insertion  of  a  strong  positive  lens  to  be 
placed  in  front  of  the  second  eye  of  the  patient.  This  would  be 
used  only  in  cases  of  probable  hyperopia  with  ciliary  spasm. 
Its  purpose  is  to  relax  the  muscle  of  accommodation  in  the 
second  eye  and,  by  fixing  of  that  eye  upon  some  exterior  ob- 
ject at  a  distance,  upon  the  principle  of  association  known  to 
exist  between  accommodation  and  convergence,  to  control  the 
accommodation  of  the  eye  under  examination. 

Fig.  70  shows  a  skiascope  invented  by  Dr.  F.  G.  Murphy, 
of  Kansas  City.  The  model  consists  mainl)'  of  a  revolving 
disc,  22  inches  in  diameter,  containing  34  lenses.  This  disc  is 
placed  at  the  end  of  a  horizontal  rod,  which  rests  on  a  fulcrum 
and  enables  the  operator  to  move  the  lens  in  front  of  the 
patient's  eye  in  any  direction.  There  are  17  plus  and  17  minus 
lenses.    An  improved  chin-rest  is  another  feature. 

THE   RETINO-SKIAMETER. 

Fig.  71  shows  an  instrument  invented  by  A.  Jay  Cross,  of 
New  York,  for  use  in  connection  with  the  skiascopic  mirror. 
It  has  been  named  a  retino-skiameter, which  expresses  its  func- 
tion as  a  retinal  shadow  measure.  As  the  illustration  shows,  it 
resembles  in  shape  a  long-handled  opera  glass  and  is  some- 
what similarly  operated.  The  purposes  which  it  is  intended  to 
serve  are  (i)  to  increase  the  size  of  the  pupil  so  that  it  can  be 
distinctly  seen  at  a  distance  of  one  or  more  meters  away;  (2) 
to  overcome  extraneous  light-reflections  without  interfering 


SKIASCOPIC    DEVICES   AND    INVENTIONS.  209 

with  the  refractive  value  of  the  lens  used,  and  (3)  to  control 
the  strength  of  the  spherical  and  cylindrical  lenses  desired. 

The  magnification  or  apparent  enlargement  of  the  pupil  is 
a  condition  much  to  be  desired  by  the  skiascopist  in  certain 
cases,  and  Mr.  Cross  claims  that  his  invention  will  effect  such 


Fig.  71. 

enlargement.  The  use  of  the  retino-skiameter  will  also  permit 
the  skiascopist  to  remain  at  a  fixed  distance  from  the  patient, 
and  he  is  thus  enabled  to  note  any  slight  rotation  in  lens 
power  without  having  to  alter  his  position  in  order  to  change 
the  lenses.  With  one  hand  the  skiascopist  controls  the  mirror, 
and  with  the  other  he  governs  the  lens  power  of  the  retino- 
skiameter. 

THE   DE   ZENG   LUMINOUS   RETINOSCOPE. 

An  improved  retinoscope,  invented  and  manufactured 
by  Henry  De  Zeng,  is  shown  in  the  illustration  on  the  next 
page.  Among  the  imperfections  of  retinoscopes  have  been 
insufficient  illumination  and  consequent  difficulty  in  getting 
a  good  reflex,  and  trouble  in  connecting  the  mirror  and  the 
light  for  the  purpose  of  illumination.  The  new  retinoscope 
has  everything  combined,  mirror,  light  and  electric  battery. 
The  instrument,  as  shown  in  the  cut,  has  a  mirror  and  small 
electric  light  of  2-candle  power;  the  two  being  so  nicely  and 
ingeniously  fixed  together  that  the  operator,  looking  from 


2IO  SKIASCOPIC    DEVICES   AND    INVENTIONS. 

behind  the  screen,  can  easily  see  and  examine  the  eye,  which 
is  nicely  illuminated.  The  condensing  lens,  located  between 
the  electric  lamp  and  the  reflector,  being  adjustable,  as  shown 
in  the  illustration,  the  effect  of  either  a  plane  or  concave 


mirror  can  be  readily  obtained,  with  any  size  light  beam  de- 
sired. As  the  electric  light  in  the  retinoscope  can  be  given 
more  or  less  current  through  the  adjustment  of  its  regulator, 
a  bright,  medium  or  faint  illumination  can  be  had  at  will. 


APPENDIX. 


Abbreviations,  Symbols  and  Designating  Letters. 


Area  i The  luminous  area. 

Area  2 The  skiascopic  mirror. 

Area  3 The  retina  of  the  observed  eye. 

Area  4 The  retina  of  the  observing  eye. 

Ace The  accommodation. 

B.  E Both  eyes. 

Cm Curvometer. 

cm Centimeter. 

D Diopter. 

D.  P Dynamic  Power. 

Interval  i . .  Space  from  area  i  to  area  2. 
Interval  2.  .Space  from  area  2  to  area  3. 
Interval  3.. Space  from  area  3  to  area  4. 

m Meter. 

mm Millimeter. 

S.  P Static  povirer. 

a Coefificient  of  wave  speed  or  of  wave  length  in  air. 

6 Coefficient   of  wave  speed   or  wave   length   in   refracting 

medium  (a?). 

c Difference  (o-^)  between  a  and  &• 

c/6 Ratio  of  resistance  in  x  to  resistance  in  air  =:  index  of 

refraction. 

c/a Ratio  of  curvature  to  dioptry  at  anterior  surface  of  lens. 

o/h Ratio  of  curvature  to  dioptry  at  both  surfaces  of  lens. 

I  -\-  cfb Equivalent  of  a/6,  index  of  refraction. 

14  211 


212  APPENDIX. 

ni Designating  angle  of  incidence. 

n Designating  angle  of  refraction. 

0 Designating  angle  of  deviation. 

r Designating  surface  of  cornea. 

r' Center  of  curvature  of  >'• 

s Anterior  surface  of  crystalline  lens. 

s' Center  of  curvature  of  s. 

t Posterior  surface  of  crystalline  lens. 

t' Center  of  curvature  of  t- 

X Refracting  medium. 

-   Static  dioptry  of  emmetropia. 

+ Positive  or  plus. 

— Negative  or  minus. 

= Sign  of  equality. 

3 Combined  with. 

:  Ratio,  or  sign  of  division. 

::  Proportion,  or  sign  of  equality. 

■J./ Radical  sign,  indicating  square  root  of  number  under. 


Glossary  of  Optical  Terms. 


Aberration (i)  Spherical  aberration  is  the  difference  in  refrac- 
tive effect,  and  therefore  of  the  position  of  the  focus  for 
different  points  in  one  meridian  of  a  spherical  lens. 

(2)  Chromatic  aberration  is  an  effect  analagous  to  chem- 
ical action  at  each  point  in  a  refracting  surface,  by  which  each 
point  in  a  wave,  or  its  energy,  is  dissolved  or  separated  into 
chromatic  or  color  elements. 

(3)  Astigmatic  "s^i^xxdlxov^.     See  "  astigmatism." 

Accommodation — The  capacity  of  the  eye  to  increase  and 
decrease  its  dioptric  power  within  a  certain  range.  The 
dynamic  power  or  refraction  of  the  eye. 

Actinic  or  Aplanatic  Lens. — A  lens  so  composed  that  spherical 
and  chromatic  aberration  are  neutralized  or  reduced  to  the 
minimum. 

Aerial  Image. — An  image  in  air. 

Ametropia — That  condition  of  an  eye,  or  of  its  dioptric  media 
in  which  its  static  refraction  is  pot  adapted  to  focus  neutral 
waves,  or  pencils  of  light  at  the  retina,  particularly  at  its  most 
sensitive  area,  the  macula  lutea. 

Aqueous  Humor. — The  transparent  fluid  that  fills  the  anterior 

cavity  of  the  eye-ball — that  part  between  the  cornea  in  front, 
and  the  crystalline  lens  and  suspensory  ligament  posteriorally. 

Asthenopia. — Painful  vision  due  to  excessive  use  of  the  accom- 
modation or  convergence. 

Astigmatism. — Difference  in  the  refractive  effect,  and  therefore 
of  the  focus  of  different  meridians  of  an  eye  or  lens,  due  to 
differences  of  curvature  in  the  different  meridians.  It  is 
analagous  to  spherical  aberration,  but  applies  to  different 
meridians.     See  "  aberration." 

Axis. — (i)  Principal  z.yA'5,  of  lens  is  a  straight  line  passing  through 
the  poles  of  its  two  surfaces,  and  through  the  optical  center 
and  nodal  points. 

(2)  SecoJidary  axis  of  a  lens  is  directed  anteriorally  to 
anterior  nodal  point  and  posteriorally  to  posterior  nodal  point, 
but  within  the  lens  passes  through  the  optical  center  between 
the  nodes. 

213 


214  GLOSSARY, 

(3)  Optic  axis  of  the  eye,  a  straight  line,  extension  of 
that  diameter  of  the  eye  which  passes  through  the  anterior 
pole  of  the  eye  or  center  of  the  cornea. 

(4)  Visual  axis — that  line  which  joins  object  with  nodal 
point  and  yellow  spot  of  the  eye. 

Binocular  Vision The  vision  of  the  two  eyes  of  one  person  by 

which  two  retinal  images  are  fused  and  projected  as  one  object. 

Choroid. — The  middle  tunic  or  coat  of  the  eye. 

Chromatic. — Pertaining  to  color.     See  "aberration." 

Ciliary. — (i)    Ciliary  muscle — the  muscle  of  accommodation. 

(2)  Ciliary  processes — the  convolutions  of  the  anterior 
margin  of  the  choroid. 

Conjugate  Foci Points  having  such  a  position,  with  reference 

to  a  lens  or  mirror,  that  each  is  the  potential  focus  of  a  pencil 
of  light  from  the  other. 

Convergence. — The  act  of  turning  both  eyes  in  towards  a  point 
in  the  median  plane. 

Cornea. — The  transparent  anterior  coat  or  surface  of  the  eye. 

Crystalline  Lens. — The  bi-convex  lens  of  the  eye,  suspended 
between  the  aqueous  and  vitreous  humors  directly  back  of 
the  pupil. 

Curvometer. — Unit  of  curvature.  The  inverse  of  the  radius  in 
meters,  representing  the  degree  of  curvature  of  a  curved  line  or 
surface  or  the  amount  of  curvature  in  a  given  arc  or  area. 

Cylinder. — A  solid  generated  by  the  revolution  of  a  rectangle 
upon  one  side  as  an  axis  of  rotation. 

Diffusion. — The  development  upon  a  screen  of  the  waves  of  a 
system  of  pencils  of  light  when  the  screen  is  not  at  the  focal 
area  of  the  pencils. 

Diopter. — The  unit  of  refractive  power,  as  measured  by  a  lens  of 
one  meter  focus. 

Divergence. — The  separation  of  the  rays  of  a  pencil  of  light. 

Emmetropia. — That  condition  of  an  eye  and  its  dioptric  media 
in  which  its  static  refraction  focuses  neutral  waves  of  light,  or 
pencils  from  the  distant  object,  at  the  retina,  particularly  at  its 
most  sensitive  area,  the  macula  lutea. 

Focus — The  center  of  curvature  of  a  series  of  concave  waves  of 
light,  the  point  at  which  the  waves  are  naturally  transposed 
into  convex  waves  by  passing  their  center  of  curvature.  It  is 
the  assemblage  of  the  foci  of  a  system  of  pencils  of  light  from 
the  same  object  upon  a  contiguous  area  or  surface  that  consti- 


GLOSSARY.  215 

tutes  a  real  image.  At  the  focus  the  molecular  activity  at  the 
point  of  origin  of  the  waves  is  reproduced  in  character,  though 
not  in  intensity  or  degree. 

(i)    Conjugate  foci.     See  "  conjugate  foci." 

(2)  Potential  foci.  The  points  at  which  concave  waves 
are  centered,  though  modified  or  recentered  before  reaching 
them — virtual,  temporary  or  transitory,  but  not  actual  foci. 

(3)  Negative  foci.  A  term  applied,  but  with  little  pro- 
priety, to  new  centers  of  curvature  of  recentered  convex  waves. 
Also  called  virtual,  though  with  little  virtue. 

(4)  Principal  focus.  The  term  is  convenient,  though 
inappropriate,  to  express  the  focal  distance  of  neutral  pencils 
modified  by  a  plus  lens. 

Hypermetropia  or  Hyperopia. — That  condition  of  an  eye  and 
of  its  dioptric  media  in  which,  without  the  use  of  the  accom- 
modation, the  potential  foci  of  the  neutral  pencils  are  posterior 
to  the  retina. 

Index. — (i~)  Index  of  Refraction.  The  ratio  of  the  sine  of  the 
angle  of  incidence  to  the  sine  of  the  angle  of  refraction  {alb). 

(2)  Index  of  Resistance.  The  ratio  of  the  resistance  of  a 
medium  to  the  resistance  of  air  as  a  standard,  measured  by 
relative  wave  speed  or  wave  length  (^cijb). 

(3)  Index  of  Deviation. — Ratio  of  the  sine  of  the  angle 
of  refraction  to  the  sine  of  the  angle  of  deviation  {cjb'). 

(4)  Index  of  Dioptry. — R3tio  of  dioptric  power  of  lens 
to  curvature  of  glass  or  other  refracting  medium  {clb). 

Iris. — The  curtain  of  the  eye,  suspended  in  the  aqueous  humor 
between  the  cornea  and  crystalline  lens,  but  always  in  contact 
at  its  pupillary  margin,  with  anterior  surface  of  the  latter. 
It  contains  a  central  opening  or  perforation,  and  two  systems 
of  muscles,  by  which  the  opening  (pupil)  may  be  enlarged  or 
contracted.     The  iris  gives  the  eye  its  color. 

Lens. — An  optical  instrument,  usually  of  glass,  with  one  or  both 
surfaces  ground  in  spherical  or  cylindrical  form,  so  as  to  give 
it  a  dioptric  power  or  capacity  to  modify  the  curvature  of  the 
waves  of  light  transmitted  through  it.  A  compound  lens  is  a 
lens  having  a  spherical  and  a  cylindrical  face  on  opposite 
sides.     See  "  toric,  periscopic." 

Macula. — The  small  area  of  the  retina,  directly  posterior  to  the 
optical  center  of  the  eye,  known  also  as  the  yellow  spot  (the 
macula  lutea).     It  is  the  most  sensitive  area  of  the  retina. 

Major. — Larger,  and  including  minor  parts,  as  major  pencils  of 
light. 


2l6  GLOSSARY. 

Meridian. — The  arc  (usually  semi-circumference)  of  a  great  circle 
passing  through  or  to  the  poles.  It  has  the  same  curvature  as 
the  surface  in  which  it  lies. 

Meter. — The  French  unit  of  measure,  equal  to  39.37  English 
inches,  or  about  40  inches. 

Minor. — Smaller,  and  included  in  the  major,  as  minor  pencils 
of  light. 

Monocular. — Pertaining  to  one  eye  alone. 

Mydriatic. — A  drug  used  to  dilate  the  pupil  and  paralyze  the 
muscle  of  accommodation. 

Myopia. — That  condition  of  an  eye  and  of  its  dioptric  media  in 
which  its  static  refraction  focuses  neutral  pencils  of  light 
forward  of  the  retina. 

Nodal  Point. — A  point  on  the  principal  axis  of  a  lens  toward 
which  an  incident  or  emergent  ray  is  directed  to  either  side  of 
the  optical  center  of  the  lens  through  which  the  ray  passes. 

Optical  Illusion. — A  sensation  having  a  nervous  foundation,  or 
due  to  a  bona  fide  retinal  image,  or  the  motion  of  an  image 
upon  the  retina,  but  by  some  anomalous  means  not  usually 
encountered  in  nature.  The  science  and  art  of  measuring 
errors  of  refraction. 

Optometry. — The  science  and  art  of  measuring  errors  of  refraction. 

Pathology. — Pertaining  to  diseases  and  diseased  conditions. 

Periscopic. — A  lens  having  a  convex  and  a  concave  surface,  but 
of  unequal  curvatures. 

Punctum  Proximum. — The  nearest  point  of  distinct  vision  with 
full  accommodation. 

Punctum  Remotum. — The  farthest  point  from  which  rays  of 
light  must  come,  or  appear  to  come,  in  order  to  focus  at  the 
retina  of  the  resting  eye. 

Pupil. — The  round  opening  in  the  iris  through  which  pencils  of 
light  are  admitted  to  the  crystalline  lens  and  posterior  part  of 
the  eye. 

Refraction. — Modification  of  the  curvature  of  a  wave  of  light 
produced  by  the  passage  of  the  wave  from  one  medium  into 
another  of  different  resistance  or  conductivity  through  a  surface 
not  conforming  at  all  points  with  the  wave. 

Retina. — The  nervous  coat  of  the  eye  ;  the  net-work  of  nerves  ;  an 
expansion  of  the  optic  nerve,  upon  which,  in  emmetropia, 
neutral  pencils  of  light  are  focused,  producing  the  image,  and 
where  the  stimulus  of  the  focused  pencils  is  transmitted  into 
nerve  energy,  by  which  vision  is  awakened. 


GLOSSARY.  217 

Skiascope. — The  mirror  with  a  perforation  used  in  skiascopy ; 
also  applied  to  a  device  for  conveniently  and  quickly  changing 
the  lenses  before  the  eye  under  examination. 

Skiascopic  Chimney. — Chimney  of  asbestos  used  in  skiascopy 
to  limit  the  area  of  light  and  give  form  to  the  luminous  area. 

Skiascopy. — The  science  and  art  of  determining  the  refractive 
condition  of  an  eye  by  observing  objective  phenomena  in  the 
pupil  of  the  eye  examined  when  light  is  reflected  into  it  from 
a  mirror. 

Static  Refraction. — The  refraction  that  form  and  resistance  gives 
without  action  being  put  forth,  as  the  refraction  of  the  eye 
without  the  use  of  the  accommodation. 

Suspensory  Ligament. — The  ligament  by  which  the  crystalline 

lens,  enclosed  in  its  capsule,  is  suspended  back  of  the  pupil. 

Subjective. — A  test  in  which  the  vision  of  the  subject  reveals  the 
dioptry  of  the  eye,  and  therefore  a  test  in  which  the  optician 
depends  upon  the  statements  of  his  patient  as  to  what  he  sees. 

Toric. — A  surface  having  a  maximum  of  curvature  in  one  meridian 
and  a  minimum  of  curvature  in  the  meridian  at  right  angles 
to  it.  A  toric  lens  is  a  lens  so  ground  that  one  surface  is  toric. 
In  dioptric  value  it  is  equal  to  a  compound  lens  having  a 
spherical  surface  on  one  face  and  a  cylindrical  surface  on 
the  other. 

Vitreous  Humor. — The  transparent  fluid  that  fills  the  posterior 
cavity  of  the  eye,  the  space  back' of  the  crystalline  lens. 

W^aves. — Undulations  of  molecules.  A  wave  consists  of  the 
unison  of  movement  in  a  superficial  extent  of  molecules  equi- 
distant from  a  common  center  of  disturbance  or  activity. 

Zone. — A  symmetrical  area  of  a  spherical  surface  bounded  by 
great  or  small  circles  parallel  to  each  other. 


INDEX 


Aberration    .   .  65,  it",  99,  143,  146,  159,  180 

Test  of 179 

Absolute  Condition 162 

Accommodation 72,  144,  170 

Active 133 

Passive 133 

Stimulus  of 147 

Watching  the      190 

Acetylene     206 

Actinic 144 

Ametropia 25,  72,  149 

Aqueous   Humor 75 

Area  of  Reversal 30,  38,  91,  123 

Asthenopia 192 

Astigmatism 72,  139,  164,  171 

Compound  Hyperopic  ...   42,     74,  167 

Compound  Myopic 45 

Correcting 178 

Irregular 181,  182 

Mixed     45,  169 

Regular 36,  164 

Simple  Hyperopic 41,  74,  166 

Simple  Myopic 44 

Axial  Ray 55 

Axis  of  Rotation 200 

Cvlinder 169 

Visual 30 


Banded  Appearance 38,  172 

Binocular 192 


c 

Choroid 120,  134 

Ciliary 134,  147 

Concave 20,  53 

Conjugate  Foci 95 

Convergence 20,  29 

Convex 20,  53 

Cornea 75,  79 

Conical 181 

Correcting  Lenses 139 

Crain,  Dr 198 

Cross,  A.  Jay 208 

Crystalline   Lens       19,  75,  134 

Curvometer 49,  57 

Cylinders 37,  40,  59,  169 

Cross 170,  181 

Law  for 164 


D 

Data,  Official 75,  76,  77,  78 

Difl'usion 19,  60,  95 

Diopter 57,  59 

Dioptric  Media 18,  "1,  "4,  75 

Dioptry 72 

D've'gence 20 


Dvnamic ,    15,  72,  130,  131 

Ktlects 131 

Factors,  Chapter  VI 26 


Emergent 20,  126,  17a 

Emmetropia      ....      20,  71,  124,  125,  149 
Evolution 49,    83,    93 


R 

Finite 19,    5S 

Focal  Area 88,  135,  136 

Focus 23,     92,     94 

Conjugate  Foci 95 

Potential  Foci 19,  21,    95 

Fuller,  Dr 200 


H 

Handling  the  Lenses 190 

Hardv  Skiascope 197 

Hyperopia    . 21,  73,  149 


I 

Image,  Real 23,  25,  29,  55,  115 

Aerial      25,     29,  155 

Potential 123,  152,  156 

Retinal 23,    29,  55 

Virtual 27,    55,  115 

Incident  Pencil 20,  35 

Index  of  Resistance 61 

Infinity 53,  141 

Initial  Appearances 150 

Intervals 127 

Changing  the 137 

Fixing  the 202 

Inversion      28,  100  » 

Iris 55,  ISO  ' 


Jackson,  Dr 104,  151 

Jennings'  Skiascope 200 


Law  of  Wave  Curvature 49 

Of  Cylinders       164 

Of  Images 142 

Of  Wave  Speed 61 

Lens 57 

Bi-convex     51,  60 

Compound 122 

Holders 196 

Negative  or  —    ....   31,  59,  121,  160 

Periscopic 66 

Plano-convex 67,  68 


INDEX 


219 


Lens 

Positive  or  + 31,  57,  121,  160 

Primary 35 

Spherical 37,  40 

Light  on  the  Face '2.1 

Limitations 175 

Luminous  Area 15,  18,  110 


M 

Macula 71,  119,  146 

Magniticatiou 60,  102 

Major 27 

Meridan 36,  122,  164,  171 

Meter  (see  Glossary) 59 

Minor 27,     55 

Mirror 27,  113 

Centimeter 175 

Circular 18 

Concave     ....    69,  113,  163,  176,  178 

Plane  . 113,  177 

Tilting  the 27,  131 

Momentum 130 

Monocular 191 

Morton  Ophthalmqscope 200 

Motion  of  Keflex,  With    ....  15,  121,  160 

Against 15,  121,  160 

At  Luminous  Area 339 

Cause  of  Rapidity 33,  156 

Rapidity  of 32,  121,  171 

Mydriatic 190 

Myopia 20,  22,  23,  24,  34,  153 


IV 

Negative    ...       53,  56,  57,  93 

Neutral 20,  53,  56 

Neutralization 15,  57,  141 

Of  Incident  Pencils 204 

Nodal  Point 91 

Nomenclature     48,  53 

Notation 48,  59 


o 

Objective 148,  151 

Observer 17 

Observed  Eye 17,  18,  118 

Observing  Eye 17,  IS,  120 

Operating  Room 183 

Optical  Illusion 13,  122 

Opticist 17 

Optometry 14 


Pathology     182 

Pencil  of  Light 20,  47,  48,  116 

Convergent 20,  29 

Divergent      20 

Emergent  ....  20,  23,  35,  41,  116,  173 

Incident 20,  23,  35,  41,  116 

Major      27 

Minor 27 

Natural 75 

Negative       121 

Neutral 20 

Positive     121 

Periscopic 66 

Phenomenon   .   .    .  " 15,  56,  126 

Position  of  Liglil 23,  137,  146,  203 

Positive     . ,53,     57,    93,  121 

Potential  Foci 20 

Power  and  Curvature 60 


Practical  Operating I85 

Prentice  Retinoscope 205 

Proving  Results ,   ,    191 

Punctum  Proximum 73,  104 

Remotum  . 73,  104 

I'upil isl  123,'  148 

Pupillary  Display 19,  148,  171,  182 

Pupillary  Plane 123 


R 

Ratio 50,    51 

Real  Focus  or  Image    23,  25,  29,  55,  92,  115 

Reflex 15,  150 

Refracting  Surfaces      63-70,     74 

Refraction,  Static 76 

Dynamic 78,    80 

Index  of 61,    75 

Negative 56 

Of  the  Eye Chapter  III 

Positive     ; 56 

Retina 148 

Retinoscope 196 

The  Prentice 205 

Retinoscopy 196 

Retino-Skiameter 208 

Reversal 15,  31,  86,  90,  126 


Schematic  Eye 33,  193 

Scissors  Movement 158 

Sine 49,  64 

Skiascope 18,  117 

Skiascopic  Chimney Ill 

Skiascopy  ....." 16,  17 

Static      '. 15 

Factors 26,  130 

Subsidiary  Areas 126 

Intervals 129 

Suggestions  to  Beginners 192 

Suspensory  Ligament .   ,   .  134 


T 

The  Initial  Condition 150 

Thorington  Eve 194 

Toric   .   .    .    .  ■ 164 

Transposition ,    53,  54 


V 

Virtual 27,  75 

Visual  Area 158 

Vitreous  Humor 75 


w 

Waves  of  Light,  Convex  20,  53,  54,  83,  125 

Concave  20,  53,  54,  125 

Natural      75 

NegatiM' 54,    94 

Neutral 20,  53,  125 

Plane 93 

Positive     54 

Spherical 48,    63 


Zone 158,  180 

Zonular 146,  158 


THE  OPTICIAN'S  MANUAL 

VOL.  I. 

By  C.  H.  Brown,  M.  D. 

Graduate  University  of  Pennsylvania  ;    Professor  of  Optics   and   Refraction  ;   formerly 

Physician  "in  Philadelphia  Hospital;  Member  of  Philadelphia  County, 

Pennsvlvauia  State  and  American  Medical  Societies. 


Chapter  I. 

Chapter  II. 

Chapter  III. 

Chapter  IV. 

Chapter  V. 

Chapter  VI. 

Chapter  VII. 

Chapter  VIII. 

Chapter  IX. 

Chapter  X. 


The  Optician's  Manual,  Vol.  I.,  has 
proved  to  be  the  most  popular  work  on 
practical  refraction  ever  published.  The 
knowledge  it  contains  has  been  more 
effective  in  building  up  the  optical  profes- 
sion than  any  other  educational  factor. 
A  study  of  it  is  essential  to  an  intelligent 
appreciation  of  \'ol.  II.,  for  it  lays  the 
foundation  structure  of  all  optical  knowl- 
edge, as  the  titles  of  its  ten  chapters  show  : 


-Introductory  Remarks. 

-The  Eye  Anatomically. 

-The  Eye  Optically ;   or,  The  Physiology  of  Vision. 

-Optics. 

-Lenses. 

-Numbering  of  Lenses. 

-The  Use  and  Value  of  Glasses. 

-Outfit  Required. 

-Method  of  Examination. 

-Presbyopia. 


The  Optician's  Manual,  Vol.  I.,  is  complete  in  itself,  and 
has  been  the  entire  optical  education  of  many  successful  opti- 
cians. For  student  and  teacher  it  is  the  best  treatise  of  its  kind, 
being  simple  in  style,  accurate  in  statement  and  comprehensive 
in  its  treatment  of  refractive  procedure  and  problems.  It  merits 
the  place  of  honor  beside  Vol.  II.  in  every  optical  library. 

Bound  in  Cloth— 422  pages— colored  plates  and  illustrations. 

Sent  postpaid  on  receipt  of  S&.OO  (8s.  4th^ 


Published  by  The  Keystone, 

THE  ORGAN  OF  THE  JEWELRY  AND  OPTIC.A.1^  TRADES, 

19TH  &  Brown  Sts.,  Philadelphia,  U.  S.  A. 


THE  OPTICIAN'S  MANUAL 

VOL.  II. 

By  C.  H.  Brown,  M.  D. 

<iraduate  University   of  Pennsylvania;   Professor  of   Optics   and   Refraction;    formerly 

Physician  in  Pliiladelphia  Hospital  ;  Member  of  Philadelphia  County, 

Pennsylvania  State  and  American  Medical  Societies. 


The  Optician's  Manual,  Vol.  II.,  is 
a  direct  continuation  of  The  Optician's 
Manual,  \'ol.  I.,  being  a  much  more 
advanced  and  comprehensive  treatise. 
It  covers  in  minutest  detail  the  four 
great  subdivisions  of  practical  eye  refrac- 
tion, viz  : 

Myopia. 
Hypermetropia. 
Astigmatism. 
Muscular  Anomalies. 


It  contains  the  most  authoritative  and  complete  researches 
tip  to  date  on  these  subjects,  treated  by  the  master  hand  of 
an  eminent  oculist  and  optical  teacher.  It  is  thoroughly  prac- 
tical, explicit  in  statement  and  accurate  as  to  fact.  All  refrac- 
tive errors  and  complications  are  clearly  explained,  and  the 
methods  of  correction  thoroughly  elucidated. 

This  book  fills  the  last  great  want  in  higher  refractive 
optics,  and  the  knowledge  contained  in  it  marks  the  standard 
of  professionalism. 

Bound  in  Cloth— 408  pa§:es— with  illustrations. 
Sent  postpaid  on  receipt  of  $2»00  (8Si-4«M 


Published  by  The  Keystone, 

THE  ORGAN  OK  THE  JEWEtRY  AND   OPTICAI,  TRADES, 

19TH  &  Brown  Sts.,  Philadelphia,  U.  S.  A. 


PHYSIOLOGIC  OPTICS 

Ocular  Dioptrics— Functions  of  the  Retina— Ocular 
Movements  and  Binocular  Vision 

By  Dr.  M.Tscherning 

Adjunct-Director  of  the  Laboratory  of  Ophthalmology  at  the  Sorboniie,  Paris 


AUTHORIZED  TRANSLATION 
By  Carl  Weiland,  M.D. 

Former  Chief  of  Clinic  in  the  Eye  Department  of  the  Jefferson  College  Hospital, 
Philadelphia,  Pa. 


This  is  the  crowning  work  on  physiologic  optics,  and  will  mark  a  new 
era  in  optical  study.  Its  distinguished  author  is  recognized  in  the  world 
of  science  as  the  greatest  living  authority  on  this  subject,  and  his  book 
embodies  not  only  his  own  researches,  but  those  of  the  several  hundred 
investigators  who,  in  the  past  hundred  years,  made  the  eye  their  specialty 
and  life  study. 

Tscherning  has  sifted  the  gold  of  all  optical  research  from  the  dross, 
and  his  book,  as  now  published  in  English  with  many  additions,  is  the 
most  valuable  mine  of  reliable  optical  knowledge  within  reach  of  ophthal- 
mologists, it  contains  380  pages  and  212  illustrations,  and  its  reference 
list  comprises  the  entire  galaxy  of  scientists  who  have  made  the  century 
famous  in  the  world  of  optics. 

The  chapters  on  Ophthalmometry,  Ophthalmoscopy,  Accommoda- 
tion, Astigmatism,  Aberration  and  Entoptic  Phenomena,  etc.— in  fact,  the 
entire  book  contains  so  much  that  is  new,  practical  and  necessary  that  no 
refractionist  can  afford  to  be  without  it. 

Bound  in  Cloth.    380  Pages,  212  Illustrations. 
Price,  SSvJ 


►3750-444s.-7dr^ 


Published  by  The  Keystone, 

THE   ORGAN   OF  THE  JEWELRY  AND   OPTICA!,   TRADES, 

19TH  &  Brown  Sts.,  Philadelphia,  U.  S.  A. 


OPHTHALMIC  LENSES 

Dioptric  Formulae  for  Combined  Cylindrical  Lenses, 

The  Prism-Dioptry  and  other  0ri§:inal  Papers 

By  Charles  F.  Prentice,  M.E. 


A  new  and  revised  edition  of  all  the  original  papers  of  this  noted  author,  com- 
bined in  one  volume.    In  this  revised  form,  with  the  addition  of  recent  research, 
these  standard  papers  are  of  increased  value.      Combined  for  the  first  time  in 
one  volume,  they  are  the  greatest  compilation  on  the  subject  of  lenses  extant. 
This  book  of  over  200  pages  contains  the  follov/ing  papers  :  . 

Ophthalmic  Lenses. 

Dioptric  Formulae  for  Combined  Cylrsidrical  Lenses. 

The  Prism-Dioptry. 

A  Metric  System  of  Numbering  and  Measuring  Prisms. 

The  Relation  of  the  Prisij-Diopl-ry  to  the  Meter  Angle. 

The  Relation  of  the  Prism-Dioptry  to  the  I,ens-Dioptry. 
The  Perfected  Prismometer. 
The  Prismometric  Scale. 

On  the  Practical  Execution  of  Ophthalmic  Prescriptions  involving  Prisms. 
A  Problem  in  Cemented  Bi-Focal  Lenses,  Solved  by  the  Prism-Dioptry. 
Why  Strong  Contra-Qeneric  Lenses  of  Equal   Power  Fail  to  Neutralize 

Each  Other. 
The  Advantages  of  the  Sphero=Toric  Lens. 
The  Iris,  as  Diaphragm  and  Photostat. 
The  Typoscope. 
The  Correction  of  Depleted  Dynamic  Refraction  (Presbyopia). 

Press  Notices  on  the  Original  Edition : 

OPHTHALMIC   LENSES. 


"  The  work  stands  alone,  in  its  present 
form,  a  compendium  of  the  various  laws  of 
physics  relative  to  this  subject  that  are  so 
difficult  of  access  in  scattered  treatises." — 
JVew  England  Medical  Gazette. 

"  It  is  the  most  complete  and  best  illus- 
trated book  on  this  special  subject  ever  pub- 
lished."—//o;o/oo-/ca/  Revieiv,  New  York. 


"  Of  all  the  simple  treatises  on  the  prop- 
erties of  lenses  that  we  have  seen,  this  is  in- 
comparably the  best.  .  .  .  The  teacher  of 
the  average  medical  student  will  hail  this 
little  work  as  a  great  boon  " — Archives  oj 
Ophthalmology,  edited  byH.Knapp,  M.D. 


DIOPTRIC  FORMUL.^;  FOR  COMBINED  CYLINDRICAL   LENSES. 


"  This  little  brochure  solves  the  problem 
of  combined  cylinders  in  all  its  aspects,  and 
in  a  manner  simple  enough  for  the  compre- 
hension of  the  average  student  of  ophthal- 
mology. The  author  is  to  be  congratulated 
upon  the  success  that  has  crowned  his  labors, 
for  nowhere  is  there  to  be  found  so  simple 
and  yet  so  complete  an  explanation  as  is  con- 
tained in  these  pages." — Archives  of  Oph- 
thalmology^ edited  by  H.  Knapp,  M.D. 


"  This  exhaustive  work  of  Mr.  Prentice 
is  a  solution  of  one  of  the  most  difficult  prob- 
lems in  ophthalmological  optics.  Thanks 
are  due  to  Mr.  Prentice  for  the  excellent 
manner  in  which  he  has  elucidated  a  sub- 
ject which  has  not  hitherto  been  satisfactor- 
ily explained." — The  Ophthalmic  Review, 
London. 


The  book  contains  110  Original  Diagrams.    Bound  in  cloth. 
Price,  $1.50  (6s.  3d.) 


Published  by  The  Keystone, 

THE   ORGAN   OF  THE  JEWELRY   AND   OPTICAL   TRADES, 

igxH  &  Brown  Sts.,  Philadelphia,  U.  S.  A. 


Optometric  Record  Book 


A  record  book,  wherein  to  record  optometric  examinations, 
is  an  indispensable  adjunct  of  an  optician's  outfit. 

The  Keystone  Optometric  Record  Book  was  specially  pre- 
pared for  this  purpose.  It  excels  all  others  in  being  not  only  a 
record  book,  but  an  invaluable  guide  in  examination. 

The  book  contains  two  hundred  record  forms  with  printed 
headings,  suggesting,  in  the  proper  order,  the  course  of  examina- 
tion that  should  be  pursued  to  obtain  most  accurate  results. 

Each  book  has  an  index,  which  enables  the  optician  to  refer 
instantly  to  the  case  of  any  particular  patient. 

The  Keystone  Record  Book  diminishes  the  time  and  labor 
required  for  examinations,  obviates  possible  oversights  from 
carelessness  and  assures  a  systematic  and  thorough  examination 
of  the  eye,  as  well  as  furnishes  a  permanent  record  of  all  exam- 
inations. 

Sent  postpaid  on  receipt  of  $1  .OO  (4s.  2d.) 


Published  by  The  Keystone, 

THE    ORGAN    OF    THE    JEWELRY    AND    OPTICAL    TRADES, 

19TH  &  Brown  Sts.,  Philadelphi.\,  U.S.A. 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 

Los  Angeles 

This  book  is  DUE  on  the  last  date  stamped  below. 


